Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
Benjamin McKay
证明了Calabi-Yau流形上的复抛物几何是复环面上的齐次几何。我们还对齐次紧Kähler流形上的复抛物几何进行了分类。
We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.
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Complete Calabi-Yau metrics from smoothing Calabi-Yau complete intersections
本文在非紧流形上构造完备Calabi-Yau度量，推广了Székelyhidi的工作，所得流形在无穷远处的切锥为$\mathbb{C} \times V_0$，且度量纤维具有变化复结构和可能的孤立奇点。
Calabi-Yau metrics of Calabi type with polynomial rate of convergence
本文构造了定义在光滑反典范除子补集上、以多项式速度逼近Calabi模型空间的完备Calabi-Yau度量，并证明了其在固定上同调类中的唯一性。
We use the gluing method to give a refined description of the collapsing Calabi-Yau metrics on Calabi-Yau 3-folds admitting a Lefschetz K3 fibration.
Convergence of Calabi-Yau manifolds
本文研究了Calabi-Yau流形在Kähler退化到orbifold奇点和复退化到正则奇点（包括锥状奇点）下的收敛性，以及一族Calabi-Yau流形的坍缩.
Desingularizations of Calabi-Yau 3-folds with a conical singularity
本文研究了具有以Calabi-Yau锥V为模型的锥奇点x的Calabi-Yau 3-folds M_0，构造了M_0的去奇异化，得到了以M_0为极限的紧致非奇异Calabi-Yau 3-folds的单参数族.我们所做的是选择一个以同一个锥V为模型的渐近锥卡-丘三重Y，然后在对Y应用一个相似性之后，在x处粘到M_0上。然后我们得到一个依赖于小实变量t的近似Calabi-Yau 3-folds的单参数族M_t。当t足够小时，我们证明了M_t上的近似Calabi-Yau结构可以变形为真正的Calabi-Yau结构，从而得到了M_0的去奇异化。我们的结果可以应用于解决orbifold奇异性，从而提供了一个定量描述的卡-丘度量的crepant分辨率。
In this paper, by applying Greene-Shapere-Vafa-Yau semi-flat metric, we give a new proof of closed formula of Weil-Petersson metric on moduli space of Calabi-Yau varieties.
A Cheng-Yau type estimate for the symplectic Calabi-Yau equation
本文在Donaldson猜想的辛4-流形Calabi-Yau方程框架下，证明了一个在Kähler情形中与Cheng-Yau经典估计相似的先验估计。
New equation on the low dimensional Calabi-Yau metrics
本文在紧致Kahler流形上引入了一个新的方程。这个方程的解对应于卡-丘度规。新方程不同于Calabi和Yau提出的Monge--Ampere方程。
Symplectic analog of Calabi's conjecture for Calabi--Yau threefolds
在本文中，我们陈述了一个类似的卡拉比猜想证明的丘。与经典情况的不同之处在于，我们提出了复结构的变形，而复杂的蒙日-安培方程描述了凯勒（辛）结构的变形。
Collapsing of Calabi-Yau manifolds and special lagrangian submanifolds
本文研究了特殊拉格朗日子流形的存在性与Calabi-Yau流形的坍缩之间的关系。首先，在Ricci平坦的Calabi-Yau流形中，在某些有界曲率的区域上构造了特殊的拉格朗日纤维化，并使其充分坍缩。然后，在相反的方向，它表明，存在的特殊拉格朗日子流形的小体积暗示的某些区域的周围的Calabi-Yau流形的崩溃。
Calabi-Yau manifolds and their degenerations
这是关于Calabi-Yau流形及其Ricci平坦度量的退化的一个简短的注记。
Generalized special Lagrangian fibration for Calabi-Yau hypersurfaces in toric varieties III: The smooth fibres
本文构造了复曲面簇中的Calabi-Yau超曲面的广义特殊Lagrange环面纤维化的所有光滑环面纤维。
We develop some consequences of the connection between Calabi-Yau structures and torsion-free $G_2$ structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching asymptotically cylindrical Calabi-Yau threefolds can be glued. Secondly, we give an alternative proof that the moduli space of Calabi-Yau structures on a six-dimensional real manifold is smooth, and extend it to the asymptotically cylindrical case. Finally, we prove that the gluing map of Calabi-Yau threefolds, extended between these moduli spaces, is a loc…
Form-type Calabi-Yau equations on Kähler manifolds of nonnegative orthogonal bisectional curvature
本文证明了具有非负正交双截曲率的Kähler流形上形式型Calabi-Yau方程的存在唯一性。
We improve Gross-Wilson's local estimates to global ones. As an application, we study the blow-up limits of the degenerating Calabi-Yau metrics on singular fibers.
Contact Calabi-Yau manifolds and Special Legendrian submanifolds
我们考虑了$α$ -Sasakian流形上的Calabi-Yau结构的推广。研究了一类特殊的勒让德子流形的形变，并对5维流形上的不变切触Calabi-Yau结构进行了分类。最后推广到余维$r$ .
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 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.
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.）
On a generalized Calabi-Yau equation
本文将Gromov在闭几乎Kähler流形上提出的广义Calabi-Yau方程推广到任意维，并证明了复2维情形下方程的不存在性.
Degenerations of Ricci-flat Calabi-Yau manifolds
本文是arXiv：1012.2940的续篇。进一步研究了Ricci平坦Kähler度量在Calabi-Yau流形退化下的格罗莫夫-豪斯多夫收敛.我们推广了arXiv：1012.2940中的定理1.1，去掉了Calabi-Yau簇的可解存在的条件.
Reduction of generalized Calabi-Yau structures
广义卡-丘结构是流形上的一种几何结构，它推广了卡-丘结构和辛结构的概念。鉴于Lin和Tolman在广义复情形下的一个结果，本文引入了广义Calabi-Yau流形上紧李群作用的广义矩映射的概念，并在约化空间上构造了约化的广义Calabi-Yau结构.作为应用，我们给出了广义矩映射与Bergman核之间的关系，并证明了广义Calabi-Yau流形上环面作用的Duistermaat-Heckman公式.
The form-type Calabi-Yau equation on a class of complex manifolds
该研究针对一类复流形上的形式型Calabi-Yau方程，通过定义astheno-Ricci曲率，证明了该曲率非正时方程存在解，推进了复几何中相关方程的可解性研究。
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.
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.
Hermitian Yang-Mills instantons on Calabi-Yau cones
研究并构造了Calabi-Yau锥上的非交换厄米Yang-Mills（HYM）瞬子。通过一种特殊的保等距算子，HYM方程被简化为Einstein-Kahler基上的一种新的Higgs-Yang-Mills流。对于任何二维的卡-丘锥，我们发现明确的解决方案，对应于非平凡的SU（d）HYM瞬子的流动方程。这些可以看作是卡-丘锥自旋联系的变形。
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.
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。
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。
On the Existence of Stable bundles with prescribed Chern classes on Calabi-Yau threefolds
本文证明了Douglas，Reinbacher和Yau关于Calabi-Yau三重空间上具有指定Chern类的稳定向量丛的存在性的一个猜想.为此，我们证明了椭圆纤维Calabi-Yau三重上某些稳定的向量丛扩张的存在性.
Simply Connected Symplectic Calabi-Yau 6-Manifolds
本文利用Gompf的辛纤维和算子沿$T^4$构造了单连通辛Calabi-Yau 6-流形.利用我们的构造，我们还得到了具有基本群$\Z$的辛非Kähler Calabi-Yau 6-流形.在本文中，我们还产生了第一个例子，单连通辛Calabi-Yau和非Calabi-Yau 6-流形，通过共各向同性Luttinger手术。
New Examples of Stable Bundles on Calabi-Yau Threefolds
本文利用丛扩张的方法构造了Calabi-Yau三重上的稳定丛。这个构造适用于任何给定的卡-丘三重方程，其中h^{1，1}>1。我们给出了秩为2和秩为4的稳定丛的例子，这些稳定丛是由给定的Calabi-Yau空间的纯几何数据构造的。作为应用，我们发现其中一些束满足杂合弦异常抵消所施加的物理约束。
Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds
本文综述了我们最近在Teichmuller几何、Riemann曲面的模空间和Calabi-Yau流形几何方面的新结果。
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。
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.
Continuity of Extremal Transitions and Flops for Calabi-Yau Manifolds
本文研究了Calabi-Yau流形上Ricci平坦Kähler度量在代数几何运算下的行为：极值变换或翻转。我们证明了Candelas和de la Ossa猜想的一个版本：与极值变换和翻转相关的Ricci平坦Calabi-Yau流形可以通过由连续的Ricci平坦Calabi-Yau流形族和Gromov-Hausdorff拓扑中的紧度量空间组成的路径连接。在证明主要结果的一个重要步骤中，建立了Calabi-Yau流形上Ricci平坦Kähler度量沿光滑的收敛性，这是一个独立的结果.
We show that Calabi-Yau manifolds are emergent from the commutative limit of six-dimensional noncommutative Hermitian U(1) instantons. Therefore we argue that the noncommutative Hermitian U(1) instantons correspond to quantized Calabi-Yau manifolds.
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.
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