Gauss-Bonnet-Chern theorem on moduli space

Details Gauss-Bonnet-Chern theorem on moduli space Gauss-Bonnet-Chern theorem on moduli space

2009-02-23

arxiv.org/abs/0902.3839v1

Mathematics

Differential Geometry

Scientific paper

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).

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