Yalong Cao, Naichung Conan Leung
We study orientability issues of moduli spaces from gauge theories on Calabi-Yau manifolds. Our results generalize and strengthen those for Donaldson-Thomas theory on Calabi-Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing problem in DT theory.
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Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
本文指出先前关于Spin(7)-瞬子与Calabi-Yau 4-流形凝聚层模空间可定向性的主要定理存在错误，SU(3)为反例，并建议读者参考Joyce-Upmeier的新理论。
Calabi-Yau coverings over some singular varieties and new Calabi-Yau 3-folds with Picard number one
本文是关于某些奇异簇容许Calabi-Yau覆盖的观察的报告。作为应用，我们构造了18个新的Picard数为1的Calabi-Yau 3-折叠，它们具有一些有趣的性质.
The aim of this article is to report on recent progress in understanding mirror symmetry for some non-complete intersection Calabi-Yau threefolds. We first construct four new smooth non-complete intersection Calabi-Yau threefolds with h^{1,1}=1, whose existence was previously conjectured by C. van Enckevort and D. van Straten. We then compute the period integrals of candidate mirror families of F. Tonoli's degree 13 Calabi-Yau threefold and three of the new Calabi-Yau threefolds. The Picard-Fuchs equations coincide with the expected Calabi-Yau equations. Some of the mirror families turn out to…
Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds.
In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group $\Z$. In this paper, we also produce the first examples of simply connected symplectic Calabi-Yau and non-Calabi-Yau 6-manifolds via coisotropic Luttinger surgery.
We prove a generalization of Bogomolov-Tian-Todorov theorem to Calabi-Yau categories.
For any toric Calabi-Yau 3-orbifold with transverse A-singularities, we prove Ruan's crepant resolution conjecture and the Gromov-Witten/Donaldson-Thomas correspondence.
A simple proof of Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds
证明了局部复曲面Calabi-Yau流形的Gopakumar-Vafa猜想。证明了给定类的局部Gopakumar-Vafa不变量在广义亏格上为零。
We discuss Calabi-Yau and fractional Calabi-Yau semiorthogonal components of derived categories of coherent sheaves on smooth projective varieties. The main result is a general construction of a fractional Calabi-Yau category from a rectangular Lefschetz decomposition and a spherical functor. We give many examples of application of this construction and discuss some general properties of Calabi-Yau categories.
Hasse-Witt invariants of Calabi-Yau varieties
本文通过Cartier算子和Calabi-Yau模形式理论定义Calabi-Yau变种的Hasse-Witt不变量，并提出两者等价的猜想，提供了多个例子支持该猜想。
On Stokes Matrices of Calabi-Yau hypersurfaces
考虑了Calabi-Yau超曲面的Picard-Fuchs微分方程的拉普拉斯变换，并计算了它们的Stokes矩阵.我们还介绍了Gel'fand-Kapranov-Zelevinski超几何系统的两种不同类型的拉普拉斯变换。
The concept of non-Gorenstein involutions on Calabi-Yau threefolds is a higher dimensional generalization of non-symplectic involutions on $K3$ surfaces. We present some elementary facts about Calabi-Yau threefolds with non-Gorenstein involutions. We give a classification of the Calabi-Yau threefolds of Picard rank one with non-Gorenstein involutions whose fixed locus is not zero-dimensional.
This note studies the equivalencies among convergences of Ricci-flat Kähler-Einstein metrics on Calabi-Yau manifolds, cohomology classes and potential functions.
We study a class of graded algebras obtained from Ore extensions of graded Calabi-Yau algebras of dimension 2. It is proved that these algebras are graded Calabi-Yau and graded coherent. The superpotentials associated to these graded Calabi-Yau algebras are also constructed.
How to tell you're hearing a Calabi-Yau: Universal variations of Hodge structure and local Schottky relations for Calabi-Yau manifolds
一个修订本，有一些更正和改进。
Holomorphic Cartan geometries and Calabi--Yau manifolds
证明了具有全纯Cartan几何的Calabi-Yau射影流形是阿贝尔簇. (Nous démontrons que les seules variétés projectives de Calabi--Yau qui possèdent des géométrie holomorphes de Cartan sont les variétés abéliennes.）
Rigidity for Families of Polarized Calabi-Yau Varieties
本文研究了极化Calabi-Yau簇的类似Shafarevich猜想。我们使用Hodge结构和Higgs束的变化来建立一个标准的{ \it刚性}的家庭。然后，我们应用该准则得到一些重要的和典型的Calabi-Yau簇族是刚性的，例如，Calabi-Yau簇的Lefschetz簇，{ \it强退化}簇（不仅限于Calabi-Yau簇的簇），允许退化为{ \it极大幂单值性}的Calabi-Yau簇的簇。
This paper is a sequel to arXiv:1012.2940. We further investigate the Gromov-Hausdorff convergence of Ricci-flat Kähler metrics under degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in arXiv:1012.2940 by removing the condition on existence of crepant resolutions for Calabi-Yau varieties.
New examples of affine Calabi-Yau 3-folds with maximal volume growth
本文构造了完整的Calabi-Yau度量的例子，这些例子是三维Calabi-Yau锥的平滑，不是低维Calabi-Yau锥的产品，并且在顶点外有orbifold奇点。
We construct a family of Calabi-Yau metrics on $\C^3$ with properties analogous to the Taub-NUT metric on $\C^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.
Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind of construction method of Calabi-Yau manifolds by pasting two non-compact Calabi-Yau manifolds. We will also in some details explain a curious and mysterious similarity with construction of some $G_2$-manifolds (also called Joyce manifolds), which are base spaces for M-theory.
We construct non-Kähler simply connected Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers by smoothing normal crossing varieties with trivial dualizing sheaves.
We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi-Yau threefold. For this purpose we prove the existence of certain stable vector bundle extensions over elliptically fibered Calabi-Yau threefolds.
Calabi-Yau construction by smoothing normal crossing varieties
研究了Calabi-Yau流形的一种构造方法，即光滑正规交叉簇的方法.我们发展了一些理论计算的Picard群的Calabi-Yau流形获得这种方法。一些应用包括，如建设新的例子Calabi-Yau 3-folds与皮卡德数1与一些有趣的性质。
Sheng and Zuo's characteristic forms are invariants of a variation of Hodge structure. We show that they characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over (Hermitian symmetric) tube domains.
Orientations for DT invariants on quasi-projective Calabi-Yau 4-folds
本文研究拟射影 Calabi-Yau 4 流形上 DT 不变量的定向问题，通过紧化与规范理论定向构造，证明了模叠的可定向性，并推广至稳定对与 Hilbert 概形。
On the Hodge Metric of the Universal Deformation Space of Calabi-Yau Threefolds
本文用Weil-Petersson度量及其里奇曲率来表示极化Calabi-Yau三重模空间上的Hodge度量。
Calabi--Yau threefolds with infinitely many divisorial contractions
我们研究了具有无穷多个整除收缩的Calabi-Yau 3-folds。我们还提出了用无限自同构群描述Calabi-Yau 3-折叠的方法。
Primitive Calabi-Yau Threefolds
一个本原的卡-丘三重是一个非奇异的卡-丘三重，它不能写成卡-丘三重退化的奇异纤维的一个可破分解。这些应该被认为是最基本的卡-丘流形;所有其他的流形都应该通过这些流形的退化而产生。本文首先继续研究具有典型奇点的Calabi-Yau三折叠的光滑性，这是作者在前一篇论文中开始的。''（alg-geom 9506022）.若X'是非奇异的三重Calabi-Yau图，f：X'->X是一个因子到曲线的收缩，我们得到了X何时可光滑的结果.然后，我们讨论了这一结果的原始卡-丘三重分类的应用。将本文的形变理论结果与“形变Calabi-Yau三重”的结果相结合，得到了对本原Calabi-Yau三重类的强限制.我们还推测如何这样的工作可能会产生的结果连接在一起的所有模空间的卡-丘三倍。
In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable bundles of rank 2 and 4 constructed out of pure geometric data of the given Calabi-Yau space. As an application, we find that some of these bundles satisfy the physical constraint imposed by heterotic string anomaly cancellation.
We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.
The art of finding Calabi-Yau differential eq1uations
讨论了求卡-丘微分方程的各种方法。
Uniform Skoda integrability and Calabi-Yau degeneration
本文研究 Calabi-Yau 流形的极化代数退化，通过证明一致 Skoda 型估计和一致 $L^\infty$-估计作出贡献。
We prove that the irreducible components of the moduli space of polarized Calabi-Yau pairs are projective.
Examples of Calabi-Yau 3-manifolds with complex multiplication
我们给出了具有复乘的Calabi-Yau三维流形的一些具体例子。
This is a survey article of the recent progresses on the metric behaviour of Ricci-flat Kähler-Einstein metrics along degenerations of Calabi-Yau manifolds.
Unobstructedness of Calabi-Yau OrbiKleinfolds
我们证明了具有某些类型的超曲面-商奇点的Calabi-Yau空间具有通畅的变形。这特别适用于所有余维为2的非奇异卡-丘orbifolds。
In this article, we summarize combinatorial description of complete intersection Calabi-Yau threefolds in Hibi toric varieties. Such Calabi-Yau threefolds have at worst conifold singularities, and are often smoothable to non-singular Calabi-Yau threefolds. We focus on such non-singular Calabi-Yau threefolds of Picard number one, and illustrate the calculation of topological invariants, using new motivating examples.
We construct Calabi-Yau 3-folds as orbifolds embedded in weighted projective space in codimension 4. For each Hilbert series that is realised, there are at least two different components of Calabi-Yau 3-folds.
We classify all smooth Calabi-Yau threefolds of Picard number two that have a general hypersurface Cox ring.
We construct examples of modular rigid Calabi--Yau threefolds, which give a realization of some new weight 4 cusp forms.
On the height of Calabi-Yau varieties in positive characteristic
研究了Calabi-Yau簇的正特征不变量，特别是Artin-Mazur形式群的高度不变量.我们用Fermat和Kummer型的Calabi-Yau簇来说明这些结果。
We study Kustin-Miller unprojections between Calabi-Yau threefolds or more precisely the geometric transitions they induce. We use them to connect many families of Calabi-Yau threefolds with Picard number one to the web of Calabi Yau complete intersections. This enables us to find explicit description of a few known families of Calabi-Yau threefolds in terms of equations. Moreover we find two new examples of Calabi-Yau threefolds with Picard group of rank one, described by Pfaffian equations in weighted projective spaces.
In this survey, we discuss the state of art about the monodromy property for Calabi-Yau varieties. We explain what is the monodromy property for Calabi-Yau varieties and then discuss some examples of Calabi-Yau varieties that satisfy this property. After this recap, we discuss a possible approach to future research in this area.
We develop some methods to construct normal crossing varieties whose dual complexes are two-dimensional, which are smoothable to Calabi--Yau threefolds. We calculate topological invariants of smoothed Calabi--Yau threefolds and show that several of them are new examples.
We prove the non-vanishing conjecture for lc pairs $(X,Δ)$ when $X$ is of Calabi--Yau type.
Notes on Calabi-Yau ordinary differential equations
本文研究了Calabi-Yau微分方程的结构以及方程背后的Calabi-Yau簇的簇与算法的关系。这为Samol和van Straten最近的一篇论文中的一些观察和计算提供了解释。
We determine the Griffiths-Yukawa coupling length of the Calabi-Yau universal families coming from hyperplane arrangements.
In this note, an overview of Calabi-Yau varieties in positive characteristic is presented. Although Calabi-Yau varieties in characteristic zero are unobstructed, there are examples of Calabi-Yau threefolds in positive characteristic which cannot be lifted to characteristic zero, although one-dimensional and two-dimensional Calabi-Yau varieties, i.e., elliptic curves and K3 surfaces, are all liftable to characteristic zero. In this respect, Calabi-Yau threefolds in positive characteristic are interesting in view of deformation theory and they are still very mysterious.
This paper presents the current status on modularity of Calabi-Yau varieties since the last update in 2003. We will focus on Calabi-Yau varieties of dimension at most three. Here modularity refers to at least two different types: arithmetic modularity and geometric modularity. These will include: (1) the modularity (automorphy) of Galois representations of Calabi-Yau varieties (or motives) defined over Q or number fields, (2) the modularity of solutions of Picard--Fuchs differential equations of families of Calabi-Yau varieties, and mirror maps (mirror moonshine), (3) the modularity of generat…
Correspondences between modular Calabi--Yau fiber products
本文描述了两种构造带截面有理椭圆曲面的纤维积与某些Calabi-Yau流形之间的有限有理态射的方法。我们用它们来构造这样的纤维积，承认最多五个奇异的纤维和刚性卡拉比-丘三倍之间的对应关系。
We show the boundedness of B-pluricanonical representations of lc log Calabi-Yau pairs in dimension $2$. As applications, we prove the boundedness of indices of slc log Calabi-Yau pairs up to dimension $3$ and that of non-klt lc log Calabi-Yau pairs in dimension $4$.
Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning the behaviour of zero-cycles on self-products of Calabi-Yau varieties. This note contains some examples of Calabi-Yau fourfolds verifying Voisin's conjecture.
We show that the dual of the Cayley cone, associated to a Minkowski sum decomposition of a reflexive polytope, contains a reflexive polytope admitting a nef-partition. This nef-partition corresponds to a Calabi-Yau complete intersection in a Gorenstein Fano toric variety degenerating to an ample Calabi-Yau hypersurface in another Fano toric variety. Using the Batyrev-Borisov mirror symmetry construction, we found the mirror contraction of a Calabi-Yau complete intersection to the mirror of the ample Calabi-Yau hypersurface.
We survey recent construction of non-Kähler Calabi-Yau manifolds by smoothing SNC varieties obtained by non-trivial isomorphisms of strict Calabi-Yau manifolds. We also give a new example by smoothing an SNC 3-fold which are constructed from automorphisms of an abelian surface.
It is known that a maximal intersection log canonical Calabi-Yau surface pair is crepant birational to a toric pair. This does not hold in higher dimension: this paper presents some examples of maximal intersection Calabi-Yau pairs that admit no toric model.
Construction and examples of higher-dimensional modular Calabi-Yau manifolds
我们构造了几个高维的Calabi-Yau流形的例子，并证明了它们的模性。
In this paper, we will construct new examples of derived equivalent Calabi--Yau 3-folds with Picard number greater than one. We also study their mirror Calabi--Yau manifolds and find that they are given by Schoen's fiber products of suitable rational elliptic modular surfaces.
We prove derived equivalence of Calabi-Yau threefolds constructed by Ito-Miura-Okawa-Ueda as an example of non-birational Calabi-Yau varieties whose difference in the Grothendieck ring of varieties is annihilated by the affine line.
We study the geometry of $3$-codimensional smooth subvarieties of the complex projective space. In particular, we classify all quasi-Buchsbaum Calabi--Yau threefolds in projective $6$-space. Moreover, we prove that this classification includes all Calabi--Yau threefolds contained in a possibly singular 5-dimensional quadric as well as all Calabi--Yau threefolds of degree at most $14$ in $\mathbb{P}^6$.
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