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arXiv · 0805.3425

Siegel metric and curvature of the moduli space of curves

Elisabetta Colombo·Paola Frediani
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Abstract

We study the curvature of the moduli space M_g of curves of genus g with the Siegel metric induced by the period map. We give an explicit formula for the holomorphic sectional curvature of M_g along a Schiffer variation at a point P on the curve X, in terms of the holomorphic sectional curvature of A_g and the second Gaussian map. Finally we extend the Kaehler form of the Siegel metric as a closed current on the Deligne-Mumford compatification of M_g and we determine its cohomology class as a multiple of the first Chern class of the Hodge bundle.

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Elisabetta Colombo, Paola Frediani. 2008-05-22. Siegel metric and curvature of the moduli space of curves. https://arxiv.org/abs/0805.3425

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