Siegel metric and curvature of the moduli space of curves

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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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Algebraic Geometry, 14H10; 14h15; 14K25; 53C42; 53C55

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http://salesiana.dossiersoluciones.com/handle/123456789/161462

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0805.3425
 http://arxiv.org/abs/0805.3425

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arXiv