Projective Variety Research Articles

Syzygy Bundles of Non-complete Linear Systems: Stability and Rigidness

Let (X, L) be a polarized smooth projective variety. For any basepoint-free linear system mathcal {L}_{V} with Vsubset {{,textrm{H},}}^{0}(X,mathcal {O}_{X}(L)), we consider the syzygy bundle M_{V} as the kernel of the evaluation map Votimes mathcal {O}_{X}rightarrow mathcal {O}_{X}(L). The purpose of this article is twofold. First, we assume that M_{V} is L-stable and prove that, in a wide family of projective varieties, it represents a smooth point [M_{V}] in the corresponding moduli space mathcal {M}. We compute the dimension of the irreducible component of mathcal {M} passing through [M_{V}] and whether it is an isolated point. It turns out that the rigidness of [M_{V}] is closely related to the completeness of the linear system mathcal {L}_{V}. In the second part of the paper, we address a question posed by Brenner regarding the stability of M_{V} when V is general enough. We answer this question for a large family of polarizations of X=mathbb {P}^{m}times mathbb {P}^{n}.

Integral Points on Varieties With Infinite Étale Fundamental Group

Abstract We study integral points on varieties with infinite étale fundamental groups. More precisely, for a number field $F$ and $X/F$ a smooth projective variety, we prove that for any geometrically Galois cover $\varphi \colon Y \to X$ of degree at least $2\dim (X)^{2}$, there exists an ample line bundle $\mathscr{L}$ on $Y$ such that for a general member $D$ of the complete linear system $|\mathscr{L}|$, $D$ is geometrically irreducible and any set of $\varphi (D)$-integral points on $X$ is finite. We apply this result to varieties with infinite étale fundamental group to give new examples of irreducible, ample divisors on varieties for which finiteness of integral points is provable.

Bambu and its applications in the discovery of active molecules against melanoma

Purpose or objectiveMelanoma is one of the most dangerous forms of skin cancer and the discovery of novel drugs is an ongoing effort. Quantitative Structure Activity Relationship (QSAR) is a computational method that allows the estimation of the properties of a molecule, including its biological activity. QSAR models have been widely employed in the search for potential drug candidates, but also for agrochemicals and other molecules with applications in different branches of the industry. Here we present Bambu, a simple command line tool to generate QSAR models from high-throughput screening bioassays datasets. MethodsThe tool was developed using the Python programming language and relies mainly on RDKit for molecule data manipulation, FLAML for automated machine learning and the PubChem REST API for data retrieval. As a proof-of-concept we have employed the tool to generate QSAR models for melanoma cell growth inhibition based on HTS data and used them to screen libraries of FDA-approved drugs and natural compounds. Additionally, Bambu was compared to QSAR-Co, another automated tool for QSAR model generation. Resultsbased on the developed tool we were able to produce QSAR models and identify a wide variety of molecules with potential melanoma cell growth inhibitors, many of which with anti-tumoral activity already described. The QSAR models are available through the URL http://caramel.ufpel.edu.br, and all data and code used to generate its models are available at Zenodo (https://doi.org/10.5281/zenodo.7495214). Bambu source code is available at GitHub (https://github.com/omixlab/bambu-v2). In the benchmark, Bambu was able to produce models with higher accuracy, recall, F1 and ROC AUC when compared to QSAR-Co for the selected datasets. ConclusionsBambu is an free and open source tool which facilitates the creation of QSAR models and can be futurely applied in a wide variety of drug discovery projects.

Seshadri stratifications and standard monomial theory

We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for a standard monomial theory. In this framework, Lakshmibai-Seshadri paths for Schubert varieties get a geometric interpretation as successive vanishing orders of regular functions.

Higher dimensional algebraic fiberings of group extensions

AbstractWe prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type but not of some groups including pure braid groups and families of poly‐surface groups that are fundamental groups of complex projective varieties.

African election management bodies in the era of democratic backsliding

ABSTRACT Although democratisation has evolved unevenly across Africa since the 1990s, there has been progress in the establishment and strengthening of independent election management bodies (EMBs). Since the mid-2000s, scholars and analysts have identified a global trend toward democratic backsliding, characterised in part by the erosion of democratic institutions. Such a trend might be expected to pose significant threats to EMBs. This article contributes new insights through a review of data from the Perceptions of Electoral Integrity and Varieties of Democracy projects. While it finds wide variation in EMB performance and autonomy, there is no overall pattern of decline that might be associated with democratic backsliding in Africa. Case analysis of Ghana and Zambia further demonstrates that the challenges EMBs face are multifaceted and not only driven by anti-democratic leaders. Co-ordinated efforts are therefore needed to strengthen EMB autonomy and capacity to (re)build trust and deliver elections with integrity.

Editorial introductions.

Editorial introductions.

Cohomology of the moduli space of degree two Enriques surfaces

We compute the intersection Betti numbers of the GIT model of the moduli space of numerically polarized Enriques surfaces of degree 2. The strategy of the cohomological calculation relies on a general method developed by Kirwan to compute the cohomology of GIT quotients of projective varieties, based on the equivariantly perfect stratification of the unstable points studied by Hesselink and others and a partial resolution of singularities, called Kirwan blow-up.

Biochemical Society support in action: experiences from our community

Throughout the year, the Biochemical Society offers a programme of grants for all career stages supporting research, attendance at scientific conferences and the sponsorship of events. So far in 2023, we have awarded over £163,000 towards lab visits, seminar series, and the advancement of research. In this article, we are delighted to share a few insights from our community that highlight the variety of projects and opportunities made possible by our funding. For more information about our funding opportunities and the application process, please visit our website.

Refined unramified cohomology of schemes

We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This generalizes to cycles of arbitrary codimension previous results of Bloch–Ogus, Colliot-Thélène–Voisin, Kahn, Voisin, and Ma. We combine our approach with the Bloch–Kato conjecture, proven by Voevodsky, to show that on a smooth complex projective variety, any homologically trivial torsion cycle with trivial Abel–Jacobi invariant has coniveau $1$. This establishes a torsion version of a conjecture of Jannsen originally formulated $\otimes \mathbb {Q}$. We further show that the group of homologically trivial torsion cycles modulo algebraic equivalence has a finite filtration (by coniveau) such that the graded quotients are determined by higher Abel–Jacobi invariants that we construct. This may be seen as a variant for torsion cycles modulo algebraic equivalence of a conjecture of Green. We also prove $\ell$-adic analogues of these results over any field $k$ which contains all $\ell$-power roots of unity.

Simplicial generation of Chow rings of matroids

We introduce a presentation of the Chow ring of a matroid by a new set of generators, called “simplicial generators.” These generators are analogous to nef divisors on projective toric varieties, and admit a combinatorial interpretation via the theory of matroid quotients. Using this combinatorial interpretation, we (i) produce a bijection between a monomial basis of the Chow ring and a relative generalization of Schubert matroids, (ii) recover the Poincaré duality property, (iii) give a formula for the volume polynomial, which we show is log-concave in the positive orthant, and (iv) recover the validity of Hodge–Riemann relations in degree 1, which is the part of the Hodge theory of matroids that currently accounts for all combinatorial applications of the work of Adiprasito et al. (2018). Our work avoids the use of “flips,” the key technical tool employed in that work.

Q-stability conditions on Calabi–Yau-𝕏 categories

We introduce $q$ -stability conditions $(\sigma,s)$ on Calabi–Yau- $\mathbb {X}$ categories $\mathcal {D}_\mathbb {X}$ , where $\sigma$ is a stability condition on $\mathcal {D}_\mathbb {X}$ and $s$ a complex number. We prove the corresponding deformation theorem, that $\operatorname {QStab}_s\mathcal {D}_\mathbb {X}$ is a complex manifold of dimension $n$ for fixed $s$ , where $n$ is the rank of the Grothendieck group of $\mathcal {D}_\mathbb {X}$ over $\mathbb {Z}[q^{\pm 1}]$ . When $s=N$ is an integer, we show that $q$ -stability conditions can be identified with the stability conditions on $\mathcal {D}_N$ , provided the orbit category $\mathcal {D}_N=\mathcal {D}_\mathbb {X}/[\mathbb {X}-N]$ is well defined. To attack the questions on existence and deformation along the $s$ direction, we introduce the inducing method. Sufficient and necessary conditions are given, for a stability condition on an $\mathbb {X}$ -baric heart (that is, a usual triangulated category) of $\mathcal {D}_\mathbb {X}$ to induce $q$ -stability conditions on $\mathcal {D}_\mathbb {X}$ . As a consequence, we show that the space $\operatorname {QStab}^\oplus \mathcal {D}_\mathbb {X}$ of (induced) open $q$ -stability conditions is a complex manifold of dimension $n+1$ . Our motivating examples for $\mathcal {D}_\mathbb {X}$ are coming from (Keller's) Calabi–Yau- $\mathbb {X}$ completions of dg algebras. In the case of smooth projective varieties, the $\mathbb {C}^*$ -equivariant coherent sheaves on canonical bundles provide the Calabi–Yau- $\mathbb {X}$ categories. Another application is that we show perfect derived categories can be realized as cluster- $\mathbb {X}$ categories for acyclic quivers.

Unpacking Authoritarian Environmental Governance

Debates about whether authoritarian or democratic environmental governance have the capacity to weather the present crises tend to gloss over variation across and within regimes. Authoritarian environmental governance plays out in diverse ways; comparing across contexts can help us understand its varying outcomes. Drawing on James C. Scott’s characterization of authoritarian high modernism, I identify four dimensions along which projects of authoritarian environmental governance vary: from maximizing to optimizing desired outputs, from thin to thicker simplifications, from rigidity to constrained flexibility, and from direct coercion to cultivating compliance. Together, they comprise a phenomenon we might call authoritarian elaboration, departing from the rigidity and simplification Scott describes. I review evidence from a variety of environmental projects in China to demonstrate how authoritarian elaboration occurs in practice. Examining the reasons behind what we might call harder and softer approaches to environmental governance, as well as their impacts on people and environments, I propose hypotheses on variation in governance practices and suggest approaches to studying them.

Building Chinese city-regions under state entrepreneurialism

ABSTRACT The past decade has witnessed a variety of city-regional projects across the world. However, the geopolitical motivation or regional coalition alone cannot fully explain the actual mechanism of city-regionalism in the Chinese context. Drawing on the governance framework of state entrepreneurialism, this article distinguishes between the processes of centrally orchestrated regional imaginary and regional cooperation through multi-scalar alliances in the making of Chinese city-regions. By tracing the latest national strategy of the Yangtze River Delta regional integration and three different cases with concrete practices, this paper suggests that the recent rise of city-regionalism reflects the dynamic development of state entrepreneurialism beyond the urban scale.

Why is Mudaraba not Practiced by Islamic Banks How can Islamic Banks Apply Mudaraba Financing Method through Models

A partnership agreement known as a mudaraba is one in which one party contributes finance and the other contributes labor or skills to a joint venture. A pre-determined ratio is used to divide the gains, and the capital provider bears the losses. Due to its compliance with the principles of risk-sharing, profit-sharing, and interest prohibition, mudaraba is one of the principal sources of financing in Islamic banking. However, due to a number of difficulties and limitations, including moral hazard, adverse selection, agency issues, a lack of standardization, legal ambiguity, and regulatory concerns, mudaraba is not frequently used by Islamic banks. The purpose of this study is to investigate the factors that contribute to Islamic banks' limited use of mudaraba and to suggest some models that could help with its implementation in various fields and situations. The paper uses a qualitative methodology based on a review and analysis of the literature. The study concludes that Islamic banks can implement mudaraba using a variety of models, including deposit, investment, project, social, and hybrid mudaraba. The paper also makes some recommendations for boosting the viability and efficacy of mudaraba financing, including enhancing governance, creating a legal framework, promoting standardization and disclosure, boosting supervision and monitoring, and raising awareness and education.

Assessment of Soil Sustainability Using the LUCAS Database in the Southwest Region of Romania

To ensure soil sustainability, the European Union considers the mitigation of the ecological, social and economic impacts and the prevention of soil degradation, which is the primary source of the ecosystem. In this respect, Land Use and Coverage Area Frame Survey (LUCAS) studies aim to investigate land use at the community level to gather information necessary for the analysis of the interactions between agriculture, environment and rural landscape and to provide estimates of agricultural areas with main crops. According to data from Eurostat, between May and October 2022, through the use of digital techniques, the levels of land coverage and land use, pastures, as well as irrigation management and structural elements in the landscape, were examined on the ground throughout the European Union. Data on the agricultural environment and soil were collected in the georeferenced points belonging to a representative sample by observing and completing the field form. At the level of the southwest region of Romania, the study was based on the inspection of 274 points by taking soil samples to analyze the quality indicators and identify key species of flowering plants. Data on land coverage and use can be used for a variety of environmental and socioeconomic projects in different fields.

A REVIEW PAPER ON INDUSTRIES REVOLUTION 4.0 POWERING THE FUTURE OF HEALTH CARE SECTOR

In the age of globalisation and digitization, the ability of computers to perform tasks normally associated with intelligent beings is known as artificial intelligence (AI), which can play a critical role in assisting in dealing with every type of business and function of human resource management in a proficient and timely manner. The unparalleled data processing capabilities of AI and ML in the pharmaceutical industry serve as a harness in the enhancement and improvement of efficiency in diagnostic assistance and clinical trials, pharmaceutical marketing, foster innovation, quality control, reduce materials waste, improve production reuse, perform predictive maintenance, and improve decision-making skills. The Fourth Industrial Revolution (industries 4.0) in Health Sector implement artificial technologies to performed functions by machines and small robotic systems programmed to do human-like tasks result great potential to transform drug discovery by accelerating the research and development timeline. This technology is being adopted by many pharmaceutical companies to help with the drug discovery and development process, which will enable them to work on a variety of research-oriented projects to improve health facilities and easily cure the diseases in the future. With the development of artificial intelligence and machine learning, the pharmaceutical industry is undergoing significant advancement like decrease the time interval gap from development of a drug product to its commercialization. We will discuss the various roles of AI and ML in health care sector and challenges in this article. As a result, this clearly demonstrates that artificial intelligence has a positive impact on the pharmaceutical industries.

The Strengths and Drawbacks of E-resources in Higher Education

The use of e-resources in higher education is inexorable. E-resources help students complete a variety of assignments and projects, and you can learn from other sources. While there are many other materials that are not important for education, one needs to be extremely careful with the resources because they require intense concentration. So, both educators and pupils must focus. E-resources perform by reinforcing higher education and accomplishing educational objectives. Higher education becomes enjoyable and interesting with flexible success through electronic resources. E-resources combine online and offline resources. Apart from that, e-resources improve teaching and learning and are helpful in research activities that improve learning outcomes. Review and pay attention to the advantages and some of the challenges of electronic resources in higher education. The review selected articles published from January 2015 up to March 2021. The articles about electronic resources in higher education were taken into consideration. The findings indicate that e-theses, e-dissertations, e-journals, e-books, and conferences are useful in higher education. The study found that electronic resources are very necessary for helping lectures in the teaching and learning process. A part of those resources helps with knowledge updates for the faculty members as well as the administration. Finally, e-resources are associated with databases that help students with writing. The study recommends training and orientation before learning research activities. Having good and powerful WI-FI is needed on campus for better access to resources. Unity and motivation for those who will be accessing resources continuously.

On the integral Hodge conjecture for varieties with trivial Chow group

AbstractWe obtain examples of smooth projective varieties over ${\mathbb C}$ that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we show that there exist such examples defined over number fields.

Slope semistability and positive cones of Grassmann bundles

Let [Formula: see text] be a vector bundle of rank [Formula: see text] on a smooth complex projective variety [Formula: see text]. In this paper, we compute the nef and pseudoeffective cones of divisors on the Grassmann bundle Gr[Formula: see text] parametrizing [Formula: see text]-dimensional subspaces of the fibers of [Formula: see text], where [Formula: see text] rk([Formula: see text]), under assumptions on [Formula: see text] as well as on the vector bundle [Formula: see text]. In particular, we show that nef cone and the pseudoeffective cone of Gr[Formula: see text] coincide if and only if nef cone and pseudoeffective cone of [Formula: see text] coincide under the assumption that [Formula: see text] is a slope semistable bundle on [Formula: see text] with [Formula: see text](End([Formula: see text]))=0. We also discuss about the nefness and ampleness of the universal quotient bundle [Formula: see text] on Gr[Formula: see text].