Geometriae Dedicata

, Volume 116, Issue 1, pp 87–109 | Cite as

Deforming Curves in Jacobians to Non-Jacobians I: Curves in C(2)

  • E. Izadi
Article

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 \(\mathbb{C}^{(2)}\) of C. More precisely, given a pencil \(g_{d}^{1}\) of degree d on C, let X be the curve parametrizing pairs of points in divisors of \(g_{d}^{1}\) (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° \((g_{5}^{1}) = 3\) and C has genus 4

Keywords

Abelian variety curve Jacobian Prym moduli space of Abelian varieties deformation symmetric powers of a curve 

Mathematics Subject Classifications (2000)

14K12 14C25 14B10 14H40 

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Copyright information

© Springer 2005

Authors and Affiliations

  • E. Izadi
    • 1
  1. 1.Department of Mathematics, Boyd Graduate Studies Research CentreUniversity of GeorgiaAthensU.S.A

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