On totally geodesic submanifolds in the Jacobian locus

DOI10.1142/S0129167X15500056zbMath1312.14076arXiv1309.1022MaRDI QIDQ5245876

Alessandro Ghigi, Elisabetta Colombo, Paola Frediani

Publication date: 15 April 2015

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1022

zbMATH Keywords

second fundamental formTorelli mapmoduli space of curvestotally geodesics submanifolds

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Period matrices, variation of Hodge structure; degenerations (32G20) Jacobians, Prym varieties (14H40) Families, moduli of curves (analytic) (14H15)

Related Items (23)

Infinitely many Shimura varieties in the Jacobian locus for $g \leq 4$ ⋮ Shimura varieties in the Torelli locus via Galois coverings of elliptic curves ⋮ Shimura curves in the Prym loci of ramified double covers ⋮ On rigid compact complex surfaces and manifolds ⋮ Vector bundles on curves coming from variation of Hodge structures ⋮ On the dimension of totally geodesic submanifolds in the Prym loci ⋮ A Hodge theoretic projective structure on compact Riemann surfaces ⋮ Kodaira fibrations and beyond: methods for moduli theory ⋮ Higher dimensional Shimura varieties in the Prym loci of ramified double covers ⋮ The Oort conjecture on Shimura curves in the Torelli locus of 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 ⋮ Massey products and Fujita decompositions on fibrations of curves ⋮ Some evidence for the Coleman-Oort conjecture ⋮ Shimura varieties and abelian covers of the line ⋮ Bergman kernel and period map for curves ⋮ Symmetric spaces uniformizing Shimura varieties in the Torelli locus ⋮ Families of curves with Higgs field of arbitrarily large kernel

Cites Work

• Shimura and Teichmüller curves
• Some results on the second Gaussian map for curves
• Cyclic coverings, Calabi-Yau manifolds and complex multiplication
• Non-existence of certain closed complex geodesics in the moduli space of curves
• The infinitesimal variation of the spin abelian differentials and periodic minimal surfaces
• Superrigidity and mapping class groups
• Coleman-Oort's conjecture for degenerate irreducible curves
• Geometry of Algebraic Curves
• Siegel metric and curvature of the moduli space of curves
• On Shimura curves in the Schottky locus
• TWO MODULI SPACES OF ABELIAN FOURFOLDS WITH AN AUTOMORPHISM OF ORDER FIVE
• Fibred surfaces, varieties isogenous to a product and related moduli spaces
• The Nielsen realization problem

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