We study the curvature of the moduli space Mg of curves of genus g with the Siegel metric induced by the period map j : Mg ! Ag. We give an explicit formula for the holomorphic sectional curvature of Mg along a Schiffer variation xP , for P a point on the curve X, in terms of the holomorphic sectional curvature of Ag and the second Gaussian map. Finally we extend the K¨ahler form of the Siegel metric as a closed current on Mg and we determine its cohomology class as a multiple of lambda.
Siegel metric and curvature of the moduli space of curves / E. Colombo, P. Frediani. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 362:3(2010), pp. 1231-1246.
Siegel metric and curvature of the moduli space of curves
E. Colombo;
2010
Abstract
We study the curvature of the moduli space Mg of curves of genus g with the Siegel metric induced by the period map j : Mg ! Ag. We give an explicit formula for the holomorphic sectional curvature of Mg along a Schiffer variation xP , for P a point on the curve X, in terms of the holomorphic sectional curvature of Ag and the second Gaussian map. Finally we extend the K¨ahler form of the Siegel metric as a closed current on Mg and we determine its cohomology class as a multiple of lambda.Pubblicazioni consigliate
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