Title | Moduli of Curves and Abelian Varieties [electronic resource] : The Dutch Intercity Seminar on Moduli / edited by Carel Faber, Eduard Looijenga |
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Imprint | Wiesbaden : Vieweg+Teubner Verlag, 1999 |
Connect to | http://dx.doi.org/10.1007/978-3-322-90172-9 |
Descript | VIII, 200p. online resource |
Moduli of Abelian Varieties: A Short Introduction and Survey -- 1 Introduction -- 2 Elliptic Curves -- 3 Abelian Varieties -- 4 The Torelli Morphism -- 5 Cycles on the Moduli Space of Abelian Varieties -- 6 The Moduli Space Ag in Positive Characteristic -- 7 The Moduli Space in Mixed Characteristic -- Remarks on Moduli of Curves -- 1 Introduction -- 2 Mapping Class Groups -- 3 The Torelli Group -- 4 Moduli Spaces of Curves -- 5 Deligne-Mumford-Knudsen Completion -- 6 Covers of Moduli Stacks -- 7 Tautological Classes -- 8 Stability -- 9 A Proarithmetic Hull of the Mapping Class Group -- 10 The Witten Conjecture -- 11 Complete Subvarieties of Moduli Spaces -- 12 Intersection Theory -- 13 Stable Maps and the Virasoro Conjecture -- A Stratification of a Moduli Space of Polarized Abelian Varieties in Positive Characteristic -- 1 Introduction -- 2 Elementary Sequences and Final Filtrations -- 3 Explicit Description of Some of the Strata -- 4 Standard Types -- 5 Moving in a Stratum -- 6 The Raynaud Trick -- 7 Results -- 8 Some Questions -- Cycles on the Moduli Space of Abelian Varieties -- 1 Introduction -- 2 The Tautological Subring of Ag -- 3 The Tautological Ring of A? g -- 4 Cycle Relations from Grothendieck-Riemann-Roch -- 5 On the Torsion of the Class ? g -- 6 The Ekedahl-Oort Stratification in Positive Characteristic -- 7 The Ekedahl-Oort Strata as Degeneracy Loci -- 8 The Degeneracy Locus Uรธ and ?0(p) -- 9 The Cycle Classes of the Strata -- 10 Effectivity of Tautological Classes -- 11 Some Additional Results -- Locally Symmetric Families of Curves and Jacobians -- 1 Introduction -- 2 Background and Definitions -- 3 Homomorphisms to Mapping Class Groups -- 4 Maps of Lattices to Mapping Class Groups -- 5 Locally Symmetric Hypersurfaces in Locally Symmetric Varieties -- 6 Geometry of the Jacobian Locus -- 7 Locally Symmetric Families of Curves -- 8 Locally Symmetric Families of Jacobians -- 9 Appendix: An Example -- A Conjectural Description of the Tautological Ring of the Moduli Space of Curves -- 1 Introduction -- 2 Known Results -- 3 The Conjectures and the Evidence -- 4 Calculations -- 5 Other Relations -- Correspondences between Moduli Spaces of Curves -- 1 Introduction -- 2 Correspondences for Mapping Class Groups: Closed Surfaces -- 3 Action of the Correspondences on the Tautological Classes -- 4 Hecke Operators Attached to Finite Abelian Covers -- 5 Correspondences via Ramified Covers -- 6 Correspondences Acting on a Lie Algebra -- Fields, Strings, Matrices and Symmetric Products -- 1 Introduction -- 2 Particles, Symmetric Products and Fields -- 3 Second-quantized Strings -- 4 Light-Cone Quantization of Quantum Field Theories -- 5 Light-Cone Quantization of String Theories -- 6 Matrix Strings and Interactions -- 7 String Theories in Six Dimensions -- Addresses