Siegel metric and curvature of the moduli space of curves

Details Siegel metric and curvature of the moduli space of curves Siegel metric and curvature of the moduli space of curves

2008-05-22

arxiv.org/abs/0805.3425v1

Mathematics

Algebraic Geometry

Scientific paper

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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