Siegel metric and curvature of the moduli space of curves

DOI10.1090/S0002-9947-09-04845-4zbMath1196.14025arXiv0805.3425OpenAlexW1970584656MaRDI QIDQ3550534

Elisabetta Colombo, Paola Frediani

Publication date: 31 March 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.3425

zbMATH Keywords

Siegel spaceSchiffer variationholomorphic sectional curvature of \(M_{g}\)Kähler form of the Siegel metricmoduli space of genus \(g\) curves \(M_{g}\)principally polarized abelian varieties of dimension \(g\)

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Families, moduli of curves (algebraic) (14H10) Theta functions and abelian varieties (14K25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Families, moduli of curves (analytic) (14H15)

Related Items (17)

Shimura varieties in the Torelli locus via Galois coverings of elliptic curves ⋮ Some results on the second Gaussian map for curves ⋮ Schiffer variations and abelian differentials ⋮ A Hodge theoretic projective structure on compact Riemann surfaces ⋮ Second Gaussian maps on surfaces ⋮ Prym map and second Gaussian map for Prym-canonical line bundles ⋮ The rank of the second Gaussian map for general curves ⋮ On the bielliptic and bihyperelliptic loci ⋮ Shimura curves in the Prym locus ⋮ FUJITA DECOMPOSITION AND HODGE LOCI ⋮ A bound on the dimension of a totally geodesic submanifold in the Prym locus ⋮ On the geometry of the second fundamental form of the Torelli map ⋮ Totally geodesic subvarieties in the moduli space of curves ⋮ On some differential-geometric aspects of the Torelli map ⋮ On the second Gaussian map for curves on a K3 surface ⋮ Hyperplane sections of abelian surfaces ⋮ On totally geodesic submanifolds in the Jacobian locus

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