Geometriae Dedicata

, Volume 116, Issue 1, pp 87–109

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


  • E. Izadi
    • Department of Mathematics, Boyd Graduate Studies Research CentreUniversity of Georgia

DOI: 10.1007/s10711-005-9006-3

Cite this article as:
Izadi, E. Geom Dedicata (2005) 116: 87. doi:10.1007/s10711-005-9006-3


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


Abelian varietycurveJacobianPrymmoduli space of Abelian varietiesdeformationsymmetric powers of a curve

Mathematics Subject Classifications (2000)


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© Springer 2005