Article

# On the Curvature Tensor of the Hodge Metric of Moduli Space of Polarized Calabi-Yau Threefolds

Journal of Geometric Analysis (Impact Factor: 0.86). 06/2005; DOI: 10.1007/BF02930760

Source: arXiv

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**ABSTRACT:**In this paper, we prove a Gauss–Bonnet–Chern type theorem in full generality for the Chern–Weil forms of Hodge bundles. That is, the Chern–Weil forms compute the corresponding Chern classes. This settles a long standing problem. Second, we apply the result to Calabi–Yau moduli, and proved the corresponding Gauss–Bonnet–Chern type theorem in the setting of Weil–Petersson geometry. As an application of our results in string theory, we prove that the number of flux vacua of type II string compactified on a Calabi–Yau manifold is finite, and their number is bounded by an intrinsic geometric quantity.Mathematische Annalen · 1.38 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper it is proved that the volumes of the moduli spaces of polarized CY manifolds with respect to the Weil-Petersson metrics are finite and they are rational numbers.Communications in Analysis and Geometry 09/2004; · 0.51 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**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 rational numbers.04/2006;

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