Exceptional Collections Research Articles

Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two

Abstract In this paper, we give a complete classification of full exceptional collections, up to cyclic permutations, normalizations and mutations, on smooth toric Fano threefolds and fourfolds with Picard rank two. For such varieties, we find all the exceptional collections of maximal length and show that they are in fact full. This gives a partial answer to a conjecture in [29] and [32]. Moreover, such full exceptional collections essentially arise from Orlov’s theorem on projective bundles.

Dual exceptional collections on Lagrangian Grassmannians

We construct graded left dual exceptional collections to the exceptional collections generating the Kuznetsov-Polishchuk blocks on Lagrangian Grassmannians. As an application, we find explicit resolutions for some natural irreducible equivariant vector bundles. Bibliography: 13 titles.

Oral Literature in Brittany: A Short History of Breton Collections and Collectors

Until recently, an understanding of oral literature depended on the interpretations of scholars. Until the second half of the 18th century, popular culture was largely ignored and was even viewed with contempt by the Breton elite. Today, a considerable number of individuals and organisations are tirelessly pursuing their work in heritage preservation, which began two centuries ago. Indeed, Brittany has always been at the forefront of this movement and boasts an exceptional collection in the field of oral heritage studies. An enormous task of analysis and study of all the documentation that has been accrued awaits and there are many questions that remain unanswered: what choices were made in undertaking these collections and what were their objectives? Consciously or unconsciously, were certain approaches favored and, if so, were others consequently neglected, or omitted? Did scholars set out to confirm hypotheses they had proposed beforehand?

Femtosecond-laser-patterned origami Janus membrane toward enhanced water fog harvesting.

Fog harvesting is an effective way to relieve water shortages in arid regions; thus, improving the efficiency of fog harvesting is urgently needed for both academic research and practical applications. Here, we report an origami patterned Janus (O-P-Janus) membrane using laser-ablated copper foams inspired by origami handcraft and traditional Chinese architecture. Compared to the planar fully ablated Janus membrane, our O-P-Janus membrane, with selectively ablated rectangular areas, exhibits an exceptional water collection rate (WCR) of approximately 267%. The underlying physical mechanism of WCR enhancement is revealed and attributed to the enhanced fog adsorbing capacity on the upper superhydrophobic origami structures and the accelerated removal of accumulated droplets beneath the lower superhydrophilic V-shaped tips. This O-P-Janus membrane with excellent fog collection performance should open up a new avenue for both device designs and potential applications toward structuring-enhanced fog collection and microfluidic control platforms.

Review: A Field Guide to White Supremacy, edited by Kathleen Belew and Ramón A. Gutiérrez

Book Review| November 01 2022 Review: A Field Guide to White Supremacy, edited by Kathleen Belew and Ramón A. Gutiérrez Kathleen Belew and Ramón A. Gutiérrez, eds. A Field Guide to White Supremacy. Oakland: University of California Press, 2021. 424 pp. Paperback $24.95. Max Felker-Kantor Max Felker-Kantor MAX FELKER-KANTOR is an assistant professor of history at Ball State University and the author of Policing Los Angeles: Race, Resistance, and the Rise of the LAPD (2018). Currently, he is finishing a book manuscript on schools, race, policing, and the D.A.R.E. program. Search for other works by this author on: This Site PubMed Google Scholar California History (2022) 99 (4): 101–103. https://doi.org/10.1525/ch.2022.99.4.101 Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Cite Icon Cite Search Site Citation Max Felker-Kantor; Review: A Field Guide to White Supremacy, edited by Kathleen Belew and Ramón A. Gutiérrez. California History 1 November 2022; 99 (4): 101–103. doi: https://doi.org/10.1525/ch.2022.99.4.101 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentCalifornia History Search In his monumental 1944 study, An American Dilemma: The Negro Problem and Modern Democracy, the famed Swedish sociologist Gunnar Myrdal outlined the fundamental contradiction facing Americans at the end of World War II, that of the gulf between what he called the “American Creed,” the supposed commitment to ideals of democracy and equal opportunity, and the reality of racial discrimination and segregation. While many continue to see this gap between ideal and reality as an aberration from America’s democratic promise, the exceptional collection of essays in Kathleen Belew and Ramón A. Gutiérrez’s A Field Guide to White Supremacy demonstrate that the persistent failure to resolve this contradiction is deeply engrained in the country’s history and that the “American dilemma” is, perhaps, all but unresolvable within the structure of the United States as presently constituted. Indeed, as its chapters collectively demonstrate, the United States as both an idea and a... You do not currently have access to this content.

Gamma conjecture II for quadrics

The Gamma conjecture II for the quantum cohomology of a Fano manifold F, proposed by Galkin, Golyshev and Iritani, describes the asymptotic behavior of the flat sections of the Dubrovin connection near the irregular singularities, in terms of a full exceptional collection, if there exists, of \({\mathcal {D}}^b(F)\) and the \({\widehat{\Gamma }}\)-integral structure. In this paper, for the smooth quadric hypersurfaces we prove the convergence of the full quantum cohomology and Gamma II. For the proof, we first give a criterion on Gamma II for Fano manifolds with semisimple quantum cohomology, by Dubrovin’s theorem of analytic continuations of semisimple Frobenius manifolds. Then we work out a closed formula of the Chern characters of spinor bundles on quadrics. By the deformation-invariance of Gromov–Witten invariants we show that the full quantum cohomology can be reconstructed by its ambient part, and use this to obtain estimations. Finally we complete the proof of Gamma II for quadrics by explicit asymptotic expansions of flat sections corresponding to Kapranov’s exceptional collections and an application of our criterion.

Proper connective differential graded algebras and their geometric realizations

We show that every proper connective dg algebra A admits a geometric realization (as defined by Orlov) by a smooth projective scheme with a full exceptional collection. If A is moreover smooth, we compute the noncommutative Chow motive of A. We go on to analyse the relationship between smoothness and regularity in more detail as well as commenting on smoothness of the degree zero cohomology for smooth proper connective dg algebras.

Orthogonal exceptional collections from -Gorenstein degeneration of surfaces

We consider a surface that admits a -Gorenstein degeneration to a cyclic quotient singularity After assuming several technical conditions, we construct d exceptional vector bundles of rank n which are orthogonal to each other.

Bursts of Genomic Instability Potentiate Phenotypic and Genomic Diversification in Saccharomyces cerevisiae.

How microbial cells leverage their phenotypic potential to survive in a changing environment is a complex biological problem, with important implications for pathogenesis and species evolution. Stochastic phenotype switching, a particularly fascinating adaptive approach observed in numerous species across the tree of life, introduces phenotypic diversity into a population through mechanisms which have remained difficult to define. Here we describe our investigations into the mechanistic basis of colony morphology phenotype switching which occurs in populations of a pathogenic isolate of Saccharomyces cerevisiae, YJM311. We observed that clonal populations of YJM311 cells produce variant colonies that display altered morphologies and, using whole genome sequence analysis, discovered that these variant clones harbored an exceptional collection of karyotypes newly altered by de novo structural genomic variations (SVs). Overall, our analyses indicate that copy number alterations, more often than changes in allelic identity, provide the causative basis of this phenotypic variation. Individual variants carried between 1 and 16 de novo copy number variations, most of which were whole chromosomal aneuploidies. Notably, we found that the inherent stability of the diploid YJM311 genome is comparable to that of domesticated laboratory strains, indicating that the collections of SVs harbored by variant clones did not arise by a chronic chromosomal instability (CIN) mechanism. Rather, our data indicate that these variant clones acquired such complex karyotypic configurations simultaneously, during stochastic and transient episodes of punctuated systemic genomic instability (PSGI). Surprisingly, we found that the majority of these highly altered variant karyotypes were propagated with perfect fidelity in long-term passaging experiments, demonstrating that high aneuploidy burdens can often be conducive with prolonged genomic integrity. Together, our results demonstrate that colony morphology switching in YJM311 is driven by a stochastic process in which genome stability and plasticity are integrally coupled to phenotypic heterogeneity. Consequently, this system simultaneously introduces both phenotypic and genomic variation into a population of cells, which can, in turn perpetuate population diversity for many generations thereafter.

A New PEDOT Derivative for Efficient Organic Solar Cell with a Fill Factor of 0.80

AbstractAlthough PEDOT:PSS is the most prominently used conducting polymer as hole transporting layer (HTL) material in organic solar cells (OSCs), the strong acidity of PEDOT:PSS has been proved to cause corrosion on electrodes, which is largely responsible for device instability. At present, the development of a non‐corrosive and stable PEDOT with comparable performance to PEDOT:PSS remains a great challenge in the field. Herein, a solid n‐PEDOT:POM powder with neutral pH is synthesized by utilizing polyoxometalate (POM) as an oxidizing reagent, which exhibits excellent water solubility, high chemical stability, and superior hole collection ability. Impressively, an amazing fill factor of 0.80 along with a photovoltaic efficiency of 17.62% is obtained in the OSC by using n‐PEDOT:POM as the HTL, suggesting an exceptional hole collection ability for n‐PEDOT:POM. In addition, the neutral pH of PEDOT:PSS effectively improves the long‐term stability of OSCs. X‐ray photoelectron spectroscopy results reveal that, compared to the electrode/PEDOT:PSS interface, the permeation of dissociative indium from the electrode to n‐PEDOT:POM can be greatly retarded, which proves the non‐corrosive effect of n‐PEDOT:POM and its improvement of device stability. The successful preparation of a non‐corrosive and stable PEDOT derivative without sacrificing its hole collection ability provides the most fruitful new insight into developing high‐performance HTL materials.

Graded matrix factorizations of size two and reduction

We associate a complete intersection singularity to a graded matrix factorization of size two of a polynomial in three variables. We show that we get an inverse to the reduction of singularities considered by C. T. C. Wall. We study this for the full strongly exceptional collections in the triangulated category of graded matrix factorizations constructed by H. Kajiura, K. Saito, and the second author.

Derived categories of centrally‐symmetric smooth toric Fano varieties

AbstractWe exhibit full exceptional collections of vector bundles on any smooth, Fano arithmetic toric variety whose split fan is centrally symmetric

Crania Canaria 2.0: construyendo una colección virtual de cráneos

El Museo Canario stores a large collection of aboriginal skulls that have been essential to the study of the origin and chronology of the population of the Canary archipelago since the 19th century. Regrettably, research has been dominated by biased and racial interpretations of both bioarchaeological and cultural evidence. When scientific racism and craniometric studies were rejected, studies of the Canarian indigenous skulls variability was also abandoned without replies. However, digital technologies and virtual sciences allow us to improve research and re-evaluate old paradigms. In this work, we present a digitalisation project aiming to construct a virtual database of the indigenous Canarian skulls, using a simple method of digitalisation that is very suitable to deal with large collections- The procedure, involving a portable 3D structured light scanner has allowed us to digitally reproduce more than 400 skulls stored at Museo Canario. This work offers a wide variety of possibilities for archaeology and anthropology. The versatility of 3D digital models enables the generation of interactive documentation, educational material for digital conservation and dissemination purposes. Indeed, 3D models are easily shared and can be displayed over diverse web-based repositories and online platforms and so, creating virtual online museums. We have created a profile in Sketchfab (https://sketchfab.com/craniacanaria2.0) where we intend to upload gradually the complete virtual collection of skulls we have realised. Moreover, digital skulls can serve as research objects. We discuss the advantages of studying 3D objects in a computerised environment, which includes traditional anthropometric studies (linear measurements and angles) but also 3D geometric morphometric approaches. In fact, in future studies, we will apply 3D geometric morphometrics for reassessing skull variation of ancient Canarians going beyond old paradigms and taking into account the latest advances in archaeology, anthropology and genetics in Canarian research. Highlights:- El Museo Canario stores an exceptional human skull collection that has served as the basis for numerous studies seeking to reveal the origin and chronology of the indigenous population.- This study presents an easy methodology for obtaining digital imagery using a 3D surface scanner, which allows constructing a virtual skull collection comprising more than 400 individuals.- Virtual 3D models have numerous advantages and applications in anthropology and archaeology, not only improving research but also permitting the re-evaluation of old paradigms.

Could H.P. Lovecraft Create a Semblance of Normality?

As part of historically minorized culture, Catalan literature endured difficult periods, e.g., the Francoist regime. To imagine different worlds writing in this language was even more arduous in the 20th century because of the negative attitude towards the fantastic shared by two fundamental trends of Catalan literature up to the 1970s: Noucentisme and historical realism. Nonetheless, H.P. Lovecraft was an important reference in the Catalan non-mimetic fiction that had a certain revival in post-war times. As a step towards “normalization” of Catalan literature after Franco’s death, the writers’ collective Ofèlia Dracs published several collections of short-stories of “genre” fiction–among them Lovecraft, Lovecraft! (1981). On the one hand, this article inscribes this exceptional collection in its historical context and in the contemporary Catalan literary system; on the other, it aims to shed light on Lovecraft’s role in Ofèlia Dracs’ book, proving the projection of his extraordinary supernatural world onto it by the presence not only of Lovecraftian hypotexts in its different tales, but also of metafictional elements inherited mainly from Joan Perucho’s postmodernist writings.

“There will be no shortage of books… or money to purchase them.” Education and the Reputation of the Library of the College of Artillery in Segovia as a Scientific and Publishing Centre

Charles III arrived in Spain from Naples accompanied by a multidisciplinary team of military advisers, including Count Gazzola from Piacenza, who had already drawn up his plans for the urgent military reforms required for the artillery. These included the institutionalisation of that branch of the army and the foundation of the college for artillery officers and industrial engineers to run the military factories being taken over by the State. The most eye-catching element of this undertaking is the formation of its magnificent Enlightenment scientific library. A study of this library reveals an exceptional collection, the origins of the first books brought to the institution, the way it was organised and the military and scientific topics addressed. But its fundamental contribution can be measured in terms of results: indeed, textbooks were created for the cadets, as well as research works on military, artillery and scientific topics written by teachers from the college, and translations of important European scientific books. Finally, as a contribution to demonstrating the cost-effectiveness of the Crown’s investment in education for war, we highlight the work of three captains, showing the versatility they achieved thanks to their education at the college and their reputation outside it, in the service of society, as guiding lights of the Sociedad Económica de Amigos del País (SEAP – Economic Society of Friends of the Country) in Segovia. Without this magnificent library, the research, monographs and translations – ultimately the college’s own published works which brought it great academic credit in Enlightenment Europe – would not have been possible.

Exceptional Collection of Objects on Some Fake Projective Planes

Abstract The purpose of this article is to explain a new method to establish the existence of an exceptional collection of length three for a fake projective plane $M$ with nontrivial automorphism group, related to a conjecture of Galkin–Katzarkov–Mellit–Shinder in 2015. Our method shows that thirty fake projective planes support such a sequence, most of which are new. In particular, this provides many new $H$-phantom categories.

Vafa–Witten Invariants from Exceptional Collections

Supersymmetric D-branes supported on the complex two-dimensional base S of the local Calabi–Yau threefold \(K_S\) are described by semi-stable coherent sheaves on S. Under suitable conditions, the BPS indices counting these objects (known as generalized Donaldson–Thomas invariants) coincide with the Vafa–Witten invariants of S (which encode the Betti numbers of the moduli space of semi-stable sheaves). For surfaces which admit a strong collection of exceptional sheaves, we develop a general method for computing these invariants by exploiting the isomorphism between the derived category of coherent sheaves and the derived category of representations of a suitable quiver with potential (Q, W) constructed from the exceptional collection. We spell out the dictionary between the Chern class \(\gamma \) and polarization J on S versus the dimension vector \(\vec {N}\) and stability parameters \(\vec {\zeta }\) on the quiver side. For all examples that we consider, which include all del Pezzo and Hirzebruch surfaces, we find that the BPS indices \(\Omega _\star (\gamma )\) at the attractor point (or self-stability condition) vanish, except for dimension vectors corresponding to simple representations and pure D0-branes. This opens up the possibility to compute the BPS indices in any chamber using either the flow tree or the Coulomb branch formula. In all cases we find precise agreement with independent computations of Vafa–Witten invariants based on wall-crossing and blow-up formulae. This agreement suggests that (1) generating functions of DT invariants for a large class of quivers coming from strong exceptional collections are mock modular functions of higher depth and (2) non-trivial single-centered black holes and scaling solutions do not exist quantum mechanically in such local Calabi–Yau geometries.

No phantoms in the derived category of curves over arbitrary fields, and derived characterizations of Brauer–Severi varieties

We show that the derived category of Brauer–Severi curves satisfies the Jordan–Holder property and cannot have quasi-phantoms, phantoms or universal phantoms. In this way we obtain that quasi-phantoms, phantoms or universal phantoms cannot exist in the derived category of smooth projective curves over a field k. Moreover, we show that a n-dimensional Brauer–Severi variety is completely characterized by the existence of a full weak exceptional collection consisting of pure vector bundles of length n+1, at least in characteristic zero. We conjecture that Brauer–Severi varieties X satisfy rdimcat(X)= ind(X)−1, provided period equals index, and prove this in the case of curves, surfaces and for Brauer–Severi varieties of index at most three. We believe that the results for curves are known to the experts. We nevertheless give the proofs, adding to the literature.

Residual categories for (co)adjoint Grassmannians in classical types

In our previous paper we suggested a conjecture relating the structure of the small quantum cohomology ring of a smooth Fano variety of Picard number 1 to the structure of its derived category of coherent sheaves. Here we generalize this conjecture, make it more precise, and support it by the examples of (co)adjoint homogeneous varieties of simple algebraic groups of Dynkin types $\mathrm {A}_n$ and $\mathrm {D}_n$, that is, flag varieties $\operatorname {Fl}(1,n;n+1)$ and isotropic orthogonal Grassmannians $\operatorname {OG}(2,2n)$; in particular, we construct on each of those an exceptional collection invariant with respect to the entire automorphism group. For $\operatorname {OG}(2,2n)$ this is the first exceptional collection proved to be full.

DERIVED CATEGORIES OF THE CAYLEY PLANE AND THE COADJOINT GRASSMANNIAN OF TYPE F

For the derived category of the Cayley plane, which is the cominuscule Grassmannian of Dynkin type E6, a full Lefschetz exceptional collection was constructed by Faenzi and Manivel. A general hyperplane section of the Cayley plane is the coadjoint Grassmannian of Dynkin type F4. We show that the restriction of the Faenzi–Manivel collection to such a hyperplane section gives a full Lefschetz exceptional collection, providing the first example of a full exceptional collection on a homogeneous variety of Dynkin type F.