Compactified Jacobians and Torelli map
نویسندگان
چکیده
منابع مشابه
Compactified Jacobians and Torelli Map
We compare several constructions of compactified jacobians using semistable sheaves, semistable projective curves, degenerations of abelian varieties, and combinatorics of cell decompositions and show that they are equivalent. We give a detailed description of the ”canonical compactified jacobian” in degree g − 1. Finally, we explain how Kapranov’s compactification of configuration spaces can b...
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It was conjectured in [Nam73] that the Torelli map Mg → Ag associating to a curve its jacobian extends to a regular map from the DeligneMumford moduli space of stable curves Mg to the (normalization of the) Igusa blowup A cent g . A counterexample in genus g = 9 was found in [AB11]. Here, we prove that the extended map is regular for all g ≤ 8, thus completely solving the problem in every genus.
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Torelli space Tg (g ≥ 2) is the quotient of Teichmüller space by the Torelli group Tg. It is the moduli space of compact, smooth genus g curves C together with a symplectic basis of H1(C;Z) and is a model of the classifying space of Tg. Mess, in his thesis [12], proved that T2 has the homotopy type of a bouquet of a countable number of circles. Johnson and Millson (cf. [12]) pointed out that a ...
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It is well known that each compact orientable surface R gives rise to a simplicial complex C(R) playing in the theory of Teichmüller modular groups a role similar to the role of Tits buildings in theories of algebraic and arithmetic groups. In this paper we introduce, for each closed orientable surface S, an analogue of Tits buildings more suitable for investigation of the Torelli group I(S) of...
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ژورنال
عنوان ژورنال: Publications of the Research Institute for Mathematical Sciences
سال: 2004
ISSN: 0034-5318
DOI: 10.2977/prims/1145475446