Singular Fibers Research Articles

Smooth asymptotics for collapsing Calabi–Yau metrics

AbstractWe prove that Calabi–Yau metrics on compact Calabi–Yau manifolds whose Kähler classes shrink the fibers of a holomorphic fibration have a priori estimates of all orders away from the singular fibers. To this end, we prove an asymptotic expansion of these metrics in terms of powers of the fiber diameter, with ‐order remainders that satisfy uniform ‐estimates with respect to a collapsing family of background metrics. The constants in these estimates are uniform not only in the sense that they are independent of the fiber diameter, but also in the sense that they only depend on the constant in the estimate for known from previous work of the second‐named author. For , the new estimates are proved by blowup and contradiction, and each additional term of the expansion arises as the obstruction to proving a uniform bound on one additional derivative of the remainder.

Hybrid Fiber Reinforced Lightweight Concrete: Vegetal and Metalized Plastic Waste Fiber Synergy and Pull-Out Behavior

Abstract Using one or more fibers in concrete is called “hybridization.” Although single-fiber concrete offers excellent performance, concrete reinforced with hybrid fibers gains speed as the synergy between the fibers results in amplified performance. This experimental work reflects the effects of incorporating 1, 2, and 3 % untreated singular and hybrid fibers on the physical and mechanical properties of lightweight concrete (LC) at 3, 28, and 90 days. Six mixture types were used: control LC, LC containing metalized plastic waste fibers (MPWFs), LC containing date palm fibers (DPFs), LC containing sisal fibers (SFs), LC with MPWFs and DPFs (Hybrid A), and LC with MPWFs and SFs (Hybrid B). In the fresh state, fiber introduction affected all mixes’ workability and wet density, and the reduction in slump and wet density was proportional to the fiber dose. However, in the hardened state, the results indicate that compressive strength (CS) and modulus of elasticity (MOE) decreased for LC containing only plastic or SFs. However, these properties increased slightly over the long term for blends containing 1 % DPF. Excepting mixtures containing MPWFs, fiber introduction improved flexural strength (FS) for all blends containing 1 % and 2 % fibers at 28 and 90 days. The most significant gains in FS were 8 % and 4 % at 28 and 90 days, respectively, for samples containing 1 % DPF. Nevertheless, fiber hybridization improved these mechanical properties and created a positive synergy in long-term bending. At 1 % fiber dosage, CS, MOE, and FS increased respectively by 3.05, 3.10, and 8 % for Hybrid A compared with the control LC. Pull-out testing provides the best means to understand typical failure modes and assess maximum tensile strength. Consequently, microstructural analysis enabled us to examine the bonding quality at the fiber-matrix interface.

Automorphisms of moduli spaces of principal bundles over a smooth curve

For any almost-simple group [Formula: see text] over an algebraically closed field [Formula: see text] of characteristic zero, we describe the automorphism group of the moduli space of semistable [Formula: see text]-bundles over a connected smooth projective curve [Formula: see text] of genus at least [Formula: see text]. The result is achieved by studying the singular fibers of the Hitchin fibration. As a byproduct, we provide a description of the irreducible components of two natural closed subsets in the Hitchin basis: the divisor of singular cameral curves and the divisor of singular Hitchin fibers.

Preparation of a novel foamed concrete modified with carbon fiber and graphite: Mechanical, electro-magnetic and microstructural characteristics based on X-CT

In this paper, foam concrete is modified using graphite and carbon fiber as absorbents. The mechanical properties are analyzed in conjunction with hydration products, pore size distribution based on XCT test. Additionally, the resistivity, complex permittivity and complex permeability are tested. The results demonstrate that carbon fiber enhances the proportion of pores with diameters less than 200 μm in foam concrete, thereby significantly enhancing its flexural strength. Furthermore, incorporating graphite helps offset the initial retardation of sulfoaluminate cement hydration induced by carbon fibers, leading to an increase in the average pore size and a reduction in compressive strength. The incorporation of carbon fibers at a concentration of 0.6 wt% achieves the percolation threshold, akin to scenarios with singular fiber incorporation. Exceeding 2 wt% graphite content results in negligible influence on the conductivity. The synergistic integration of graphite and carbon fibers significantly improves the electromagnetic wave absorption performance of the composite. At a thickness of 6 mm, the material exhibits an effective bandwidth where the reflection loss is less than −10 dB, extending up to 2.5 GHz, which constitutes 52.08 % of the tested frequency spectrum.

Towards the Classification of Semistable Fibrations Having Exactly Five Singular Fibers

Towards the Classification of Semistable Fibrations Having Exactly Five Singular Fibers

Sections and Unirulings of Families over $\mathbb{P}^{1}$

AbstractWe consider morphisms $\pi : X \to \mathbb{P}^{1}$ of smooth projective varieties over $\mathbb{C}$. We show that if π has at most one singular fibre, then X is uniruled and π admits sections. We reach the same conclusions, but with genus zero multisections instead of sections, if π has at most two singular fibres, and the first Chern class of X is supported in a single fibre of π.To achieve these result, we use action completed symplectic cohomology groups associated to compact subsets of convex symplectic domains. These groups are defined using Pardon’s virtual fundamental chains package for Hamiltonian Floer cohomology. In the above setting, we show that the vanishing of these groups implies the existence of unirulings and (multi)sections.

Hwang-Oguiso invariants and frozen singularities in special geometry

In Special Geometry there are two inequivalent notions of “Kodaira type” for a singular fiber: one associated with its local monodromy and one with its Hwang-Oguiso characteristic cycle. When the two Kodaira types are not equal the geometry is subtler and its deformation space gets smaller (“partially frozen” singularities). The paper analyzes the physical interpretation of the Hwang-Oguiso invariant in the context of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 QFT and describes the surprising phenomena which appear when it does not coincide with the monodromy type. The Hwang-Oguiso multiple fibers are in one-to-one correspondence with the partially frozen singularities in M-theory compactified on a local elliptic K3: a chain of string dualities relates the two geometric set-ups. Paying attention to a few subtleties, this correspondence explains in purely geometric terms how the “same” Kodaira elliptic fiber may have different deformations spaces. The geometric computation of the number of deformations agrees with the physical expectations. At the end we briefly outline the implications of the Hwang-Oguiso invariants for the classification program of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs.

Compactified Jacobians of extended ADE curves and Lagrangian fibrations

We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalize Kodaira’s classification of singular elliptic fibers and thus call them extended ADE curves. On such a curve [Formula: see text], we describe a compactified Jacobian and show that its components reflect the intersection graph of [Formula: see text]. This extends known results when [Formula: see text] is reduced, but new difficulties arise when [Formula: see text] is non-reduced. As an application, we get an explicit description of general singular fibers of certain Lagrangian fibrations of Beauville–Mukai type.

An Elementary Construction of Modified Hamiltonians and Modified Measures of 2D Kahan Maps

We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials defining the prolongation of the three parallel sides of a hexagon. On the vertices of such a hexagon lie the indeterminacy points of the KHK map. This result is obtained analysing the structure of the singular fibres of the known invariant. We apply this construction to several examples, and we prove that a similar result holds true for a case outside the hypotheses of the main theorem, leading us to conjecture that further extensions are possible.

Vũ Ngọc’s conjecture on focus-focus singular fibers with multiple pinched points

Vũ Ngọc’s conjecture on focus-focus singular fibers with multiple pinched points

Resolution of singular fibers of an S1-manifold

In this paper, we present a resolution of discrete singular fibers of a closed 5-manifold equipped with a locally free S1-action, and prove its compatibility with the resolution of cyclic surface singularities in the quotient orbifold by the S1-action.

Elliptic bihamiltonian structures from relative shifted Poisson structures

AbstractIn this paper, generalizing our previous construction, we equip the relative moduli stack of complexes over a Calabi–Yau fibration (possibly with singular fibers) with a shifted Poisson structure. Applying this construction to the anticanonical linear systems on surfaces, we get examples of compatible Poisson brackets on projective spaces extending Feigin–Odesskii Poisson brackets. Computing explicitly the corresponding compatible brackets coming from Hirzebruch surfaces, we recover the brackets defined by Odesskii–Wolf.

Mirror symmetry for five-parameter Hulek-Verrill manifolds

We study the mirrors of five-parameter Calabi-Yau threefolds first studied by Hulek and Verrill in the context of observed modular behaviour of the zeta functions for Calabi-Yau manifolds. Toric geometry allows for a simple explicit construction of these mirrors, which turn out to be familiar manifolds. These are elliptically fibred in multiple ways. By studying the singular fibres, we are able to identify the rational curves of low degree on the mirror manifolds. This verifies the mirror symmetry prediction obtained by studying the mirror map near large complex structure points. We undertake also an extensive study of the periods of the Hulek-Verrill manifolds and their monodromies. On the mirror, we compute the genus-zero and -one instanton numbers, which are labelled by 5 indices, as h^{1,1}\!=5h1,1=5. There is an obvious permutation symmetry on these indices, but in addition there is a surprising repetition of values. We trace this back to an S_{6}S6 symmetry made manifest by certain constructions of the complex structure moduli space of the Hulek-Verrill manifold. Among other consequences, we see in this way that the moduli space has six large complex structure limits. It is the freedom to expand the prepotential about any one of these points that leads to this symmetry in the instanton numbers. An intriguing fact is that the group that acts on the instanton numbers is larger than S_6S6 and is in fact an infinite hyperbolic Coxeter group, that we study. The group orbits have a “web” structure, and with certain qualifications the instanton numbers are only nonzero if they belong to what we term “positive webs”. This structure has consequences for instanton numbers at all genera.

Tame or wild Toeplitz shifts

AbstractWe investigate tameness of Toeplitz shifts. By introducing the notion of extended Bratteli–Vershik diagrams, we show that such shifts with finite Toeplitz rank are tame if and only if there are at most countably many orbits of singular fibres over the maximal equicontinuous factor. The ideas are illustrated using the class of substitution shifts. A body of elaborate examples shows that the assumptions of our results cannot be relaxed.

T-equivariant disc potential and SYZ mirror construction

We develop a G-equivariant Lagrangian Floer theory and obtain a curved A∞ algebra, and in particular a G-equivariant disc potential. We construct a Morse model, which counts pearly trees in the Borel construction LG. When applied to a smooth moment map fiber of a semi-Fano toric manifold, our construction recovers the T-equivariant toric Landau-Ginzburg mirror of Givental. We also study the S1-equivariant Floer theory of a typical singular fiber of a Lagrangian torus fibration (i.e. a pinched torus) and compute its S1-equivariant disc potential via the gluing technique developed in [14,37].

Essential surfaces in Seifert fiber spaces with singular surfaces

Two-sided incompressible surfaces in Seifert fiber spaces with isolated singular fibers are well-understood. Frohman [3] and Rannard [6] have shown that one-sided incompressible surfaces in Seifert fiber spaces which have isolated singular fibers are either pseudo-horizontal or psuedo-vertical. We extend their result to characterise essential surfaces in Seifert fiber spaces which may have singular surfaces, i.e., in S1-foliated 3-manifolds which have fibered model neighbourhoods that are isomorphic to either a fibered solid torus or a fibered solid Klein bottle.

Smoothability of relative stable maps to stacky curves

Using log geometry, we study smoothability of genus zero twisted stable maps to stacky curves relative to a collection of marked points. One application is to smoothing semi-log canonical fibered surfaces with marked singular fibers.

Topology of Ambient 3-Manifolds of Non-Singular Flows with Twisted Saddle Orbit

In the present paper, nonsingular Morse – Smale flows on closed orientable 3-manifolds are considered under the assumption that among the periodic orbits of the flow there is only one saddle and that it is twisted. An exhaustive description of the topology of such manifolds is obtained. Namely, it is established that any manifold admitting such flows is either a lens space or a connected sum of a lens space with a projective space, or Seifert manifolds with a base homeomorphic to a sphere and three singular fibers. Since the latter are prime manifolds, the result obtained refutes the claim that, among prime manifolds, the flows considered admit only lens spaces.

Tekstilom armiran beton

Textile-reinforced concrete (TRC) is a reinforced concrete, where steel reinforcement is replaced with textiles or fibers. Textile reinforcement is a material consisting of natural or synthetic singular technical fibres processed into yarns or rovings which are woven into multi-axial textile fabrics having an open mesh or grid structure. In the paper an overview of tests results related to mechanical properties, deformation properties and durability characteristics of textile meshs are presented. Applications of different textiles as reinforcement in TRC is analyzed through some realized projects. TRC has been successfully employed for strengthening or repair of damaged structural elements and lightweight, thin structural elements (precast thin-walled elements, shells, tanks, pipes, pedestrian bridge, waterproofing structure, integrated cladding systems, external insulation system).

From Three Dimensional Manifolds to Modular Tensor Categories

Using M-theory in physics, Cho et al. (JHEP 2020:115 (2020) recently outlined a program that connects two parallel subjects of three dimensional manifolds, namely, geometric topology and quantum topology. They suggest that classical topological invariants such as Chern-Simons invariants of $$\text {SL}(2,{\mathbb {C}})$$ -flat connections and $$\text {SL}(2,{\mathbb {C}})$$ -adjoint Reidemeister torsions of a three manifold can be packaged together to produce a $$(2+1)$$ -topological quantum field theory, which is essentially equivalent to a modular tensor category. It is further conjectured that every modular tensor category can be obtained from a three manifold and a semi-simple Lie group. In this paper, we study this program mathematically, and provide strong support for the feasibility of such a program. The program produces an algorithm to generate the potential modular T-matrix and the quantum dimensions of a candidate modular data. The modular S-matrix follows from essentially a trial-and-error procedure. We find premodular tensor categories that realize candidate modular data constructed from Seifert fibered spaces and torus bundles over the circle that reveal many subtleties in the program. We make a number of improvements to the program based on our examples. Our main result is a mathematical construction of the modular data of a premodular category from each Seifert fibered space with three singular fibers and a family of torus bundles over the circle with Thurston SOL geometry. The modular data of premodular categories from Seifert fibered spaces can be realized using Temperley-Lieb-Jones categories and the ones from torus bundles over the circle are related to metaplectic categories. We conjecture that a resulting premodular category is modular if and only if the three manifold is a $${\mathbb {Z}}_2$$ -homology sphere, and condensation of bosons in the resulting properly premodular categories leads to either modular or super-modular tensor categories.