相关论文: Remarks on the Chern classes of Calabi-Yau moduli

In this paper, we study the Chern classes on the moduli space of polarized Calabi-Yau manifolds. We prove that the integrations of the invariants of the curvature of the Weil-Petersson metric are finite. In some special cases, they are even…

In this paper, we define and study the Weil-Petersson geometry. Under the framework of the Weil-Petersson geometry, we study the Weil-Petersson metric and the Hodge metric. Among the other results, we represent the Hodge metric in terms of…

In this paper, we represent the Hodge metric in terms of the Weil-Petersson metric and its Ricci curvature on the moduli spaces of polarized Calabi-Yau threefolds.

In this paper we proved that the Weil-Petersson volume of the Chern class of any order over the moduli space of Calabi-Yau manifolds is a rational number. We also found the necessary and sufficient condition of the incompleteness of…

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.

In this paper, we proved that the Weil-Petersson volume of Calabi-Yau moduli is a rational number. We also proved that the integrations of the invariants of the Ricci curvature of the Weil-Petersson metric with respect to the Weil-Petersson…

In this paper, we proved the Gauss-Bonnet-Chern theorem on moduli space of polarized Kahler manifolds. Using our results, we proved the rationality of the Chern-Weil forms (with respect to the Weil-Petersson metric) on CY moduli. As an…

We study the class of compact complex manifolds whose first Chern class vanishes in the Bott-Chern cohomology. This class includes all manifolds with torsion canonical bundle, but it is strictly larger. After making some elementary remarks,…

We establish an unexpected relation among the Weil-Petersson metric, the generalized Hodge metrics and the BCOV torsion. Using this relation, we prove that certain kind of moduli spaces of polarized Calabi-Yau manifolds do not admit…

A formula for the first Chern class of the Verlinde bundle over the moduli space of smooth genus g curves is given. A finite-dimensional argument is presented in rank 2 using geometric symmetries obtained from strange duality, relative…

In this paper, it is proved that the Hodge metric completion of the moduli space of polarized and marked Calabi-Yau manifolds, i.e. the Torelli space, is a complex affine manifold. As applications we prove that the period map from the…

In this paper, we study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let $U$ be a neighborhood of the moduli space. Then we know the universal covering space $V$ of $U$ is a smooth manifold. Suppose $D$ is…

Compact Vaisman manifolds with vanishing first Chern class split into three categories, depending on the sign of the Bott-Chern class. We show that Vaisman manifolds with non-positive Bott-Chern class admit canonical metrics, are…

We introduce a simple and very fast algorithm that computes Weil-Petersson metrics on moduli spaces of polarized Calabi-Yau manifolds. Also, by using Donaldson's quantization link between the infinite and finite dimensional G.I.T quotients…

We prove that any compact complex homogeneous space with vanishing first Chern class after an appropriate deformation of the complex structure admits a homogeneous Calabi-Yau with torsion structure, provided that it also has an invariant…

We give upper and lower bounds for the order of the top Chern class of the Hodge bundle on the moduli space of principally polarized abelian varieties. We also give a generalization to higher genera of the famous formula $12…

We give upper and lower bounds for the order of the top Chern class of the Hodge bundle on the moduli space of principally polarized abelian varieties.

In this paper, we give an expression and some estimates of the curvature tensor of the Hodge metric over the moduli space of a polarized Calabi-Yau threefold. The symmetricity of the Yukawa coupling is also studied. In the last section of…

We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section…

We prove that the $\ell$-adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over $\bar{ \mathbb{Q}}_p$, descend to classes in the $\ell$-adic…