Polarizations of Prym varieties of pairs of coverings
نویسندگان
چکیده
منابع مشابه
Polarizations of Prym Varieties of Pairs of Coverings
To any pair of coverings fi : X → Xi, i = 1, 2 of smooth projective curves one can associate an abelian subvariety of the Jacobian JX , the Prym variety P (f1, f2) of the pair (f1, f2). In some cases we can compute the type of the restriction of the canonical principal polarization of JX . We obtain 2 families of Prym-Tyurin varieties of exponent 6.
متن کاملPrym varieties of pairs of coverings
The Prym variety of a pair of coverings is defined roughly speaking as the complement of the Prym variety of one morphism in the Prym variety of another morphism. We show that this definition is symmetric and give conditions when such a Prym variety is isogenous to an ordinary Prym variety or to another such Prym variety. Moreover in order to show that these varieties actually occur we compute ...
متن کاملPrym Varieties of Cyclic Coverings
The Prym map of type (g, n, r) associates to every cyclic covering of degree n of a curve of genus g, ramified at a reduced divisor of degree r, the corresponding Prym variety. We show that the corresponding map of moduli spaces is generically finite in most cases. From this we deduce the dimension of the image of the Prym map.
متن کاملPolarizations of Prym Varieties for Weyl Groups via Abelianization
Let π : Z → X be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group G. For any dominant weight λ consider the curve Y = Z/Stab(λ). The Kanev correspondence defines an abelian subvariety Pλ of the Jacobian of Y . We compute the type of the polarization of the restriction of the canonical principal polarization of Jac(Y ) to P...
متن کاملDimensions of Prym Varieties
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. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2006
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-005-1279-0