On the geometry of two dimensional Prym varieties
نویسندگان
چکیده
منابع مشابه
On the Geometry of Two Dimensional Prym Varieties
If Σ is a smooth genus two curve, Σ ⊂ Pic(Σ) the Abel embedding in the degree one Picard variety, |2Σ| the projective space parametrizing divisors on Pic(Σ) linearly equivalent to 2Σ, and Pic(Σ)2 = G ∼= (Z/2Z) the subgroup of points of order two in the Jacobian variety J(Σ) = Pic(Σ), then G acts on |2Σ| and the quotient variety |2Σ|/G parametrizes two fundamental moduli spaces associated with t...
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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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Let P be the Prym variety associated with a covering π : Y → X between non-singular irreducible projective curves. If P̃ is a principally polarized Prym-Tyurin variety associated with P , we prove that the induced Abel-Prym morphism ρ̃ : Y → P̃ is birational onto its image for genus gX > 2 and deg π 6= 2. We use such result to prove that the Picard bundle over the Prym variety is simple and moreov...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1999
ISSN: 0030-8730
DOI: 10.2140/pjm.1999.188.353