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ISSN 1088-6850(e) ISSN 0002-9947(p)

Siegel metric and curvature of the moduli space of curves

Author(s): Elisabetta Colombo; Paola Frediani
Journal: Trans. Amer. Math. Soc. 362 (2010), 1231-1246.
MSC (2000): Primary 14H10, 14H15, 14K25, 53C42, 53C55
Posted: October 19, 2009
MathSciNet review: 2563728
Retrieve article in: PDF

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Abstract: We study the curvature of the moduli space ${M_g}$ of curves of genus with the Siegel metric induced by the period map $j:{ M_g}\rightarrow {A_g}$ . We give an explicit formula for the holomorphic sectional curvature of ${M_g}$ along a Schiffer variation $\xi_P$ , for a point on the curve , in terms of the holomorphic sectional curvature of ${A_g}$ and the second Gaussian map. Finally we extend the Kähler form of the Siegel metric as a closed current on $\overline{M}_g$ and we determine its cohomology class as a multiple of $\lambda$ .

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