2004/02/04 by Elham Izadi, E. Izadi, Izadi, E.
Mathematics · #14C25 #14H40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 14K12 #Secondary 14B10 #math.AG #msc:14B10 #msc:14C25 #msc:14H40 #msc:14K12
paper · pdf · doi:10.48550/arxiv.math/0402062
ams-latex, 27 pages
arxiv created 2004/02/04 · openalex publication_date 2004/02/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce deformation theoretic methods for determining when a curve X in a non-hyperelliptic jacobian JC will deform with JC to a non-jacobian. We apply these methods to a particular class of curves in symmetric powers C(e) of C where 3≤ e≤ g-3. More precisely, given a pencil g1d of degree d on C, let X be the curve parametrizing divisors of degree e in divisors of g1d (see the paper for the precise scheme-theoretical definition). Under certain genericity assumptions on the pair (C, g1d), we prove that if X deforms infinitesimally out of the jacobian locus with JC then either d=2e, dimH0 (g1d) = e or d=2e+1, dimH0 (g1d) = e+1. The analogous result in the case e=2 without genericity assumptions was proved earlier.