Gauss-Bonnet-Chern theorem on moduli space

DOI10.1007/S00208-013-0907-4zbMATH Open1287.32009arXiv0902.3839OpenAlexW2148901206MaRDI QIDQ382303

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Publication date: 18 November 2013

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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).

Full work available at URL: https://arxiv.org/abs/0902.3839

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