Deforming Curves in Jacobians to Non-Jacobians I: Curves in C(2)
نویسنده
چکیده
Abstract. We introduce deformation theoretic methods for determining when a curve X in a nonhyperelliptic Jacobian JC will deform with JC to a non-Jacobian. We apply these methods to a particular class of curves in the second symmetric power C of C. More precisely, given a pencil g1 d of degree d on C, let X be the curve parametrizing pairs of points in divisors of g1 d (see the paper for the precise scheme-theoretical definition). We prove that if X deforms infinitesimally out of the Jacobian locus with JC then either d=4 or d=5, dim H ◦(g1 5)=3 and C has genus 4.
منابع مشابه
Deforming Curves in Jacobians to Non-jacobians I: Curves in C
Jacobians of curves are the best understood abelian varieties. There are many geometric ways of constructing curves in jacobians whereas it is difficult to construct interesting curves in most other abelian varieties. In this paper and its sequels we introduce methods for determining whether a given curve in a jacobian deforms with it when the jacobian deforms to a non-jacobian. We apply these ...
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