Gauss-Bonnet-Chern theorem on moduli space

Abstract

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 application in physics, by the Ashok-Douglas theory, counting the number of flux compactifications of the type IIb string on a Calabi-Yau threefold is related to the integrations of various Chern-Weil forms. We proved that all these integrals are finite (and also rational).

Final version, Journal ref added

References in corpus (5)

• Critical points and supersymmetric vacua, III: String/M models
• Distribution of Flux Vacua around Singular Points in Calabi-Yau Moduli Space
• Finiteness of volume of moduli spaces
• On the Weil-Petersson volume and the first Chern Class of the moduli space of Calabi-Yau manifolds
• On the Geometry of Moduli Space of Polarized Calabi-Yau manifolds

Cited by in corpus (5)

• Moduli Space Holography and the Finiteness of Flux Vacua
• Taming the Landscape of Effective Theories
• Finiteness for self-dual classes in integral variations of Hodge structure
• Degenerations of Calabi-Yau threefolds and BCOV invariants
• Remarks on the Chern classes of Calabi-Yau moduli