Prym varieties and the Schottky problem
نویسندگان
چکیده
منابع مشابه
Prym varieties and the Schottky problem for cubic threefolds
A theorem of Mumford’s states that for a smooth cubic threefold X, the intermediate Jacobian JX is a principally polarized abelian variety of dimension 5 whose theta divisor has a unique singular point, which has multiplicity three. This talk describes joint work with R. Friedman, in which we prove a converse: if A is a principally polarized abelian variety of dimension 5 whose theta divisor ha...
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Given a tame Galois branched cover of curves π : X → Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg-Witten theory. ...
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is a double covering, where C and C are nonsingular complete curves with Jacobians J and 3. The involution 1: C C interchanging sheets extends to t: I J, and up to some points of order two, 3 splits into an even part J and an odd part P, the Prym variety. The Prym P has a natural polarization on it, but only in two cases where 21 has zero or two branch points do we get a unique principal polari...
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This paper gives a uniform construction of infinitely many primitive Teichmüller curves V ⊂ Mg for g = 2, 3 and 4.
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Contents 1. Introduction 2 2. Prym varieties for covers of curves 3 3. Galois covers 8 4. Degree two covers 10 5. Covers of degree three 13 6. Covers of degree four 15 6.1. The cyclic case 15 6.2. The Klein case 17 7. The dihedral case 22 7.1. The bigonal construction 34 8. The alternating case 37 8.1. The trigonal construction for the case A 4 43 9. The symmetric case 44 9.1. The classical cas...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 1977
ISSN: 0020-9910,1432-1297
DOI: 10.1007/bf01418373