Deforming curves in jacobians to non-jacobians I: curves in $C^{(2)}$
| dc.creator | Izadi, E. | |
| dc.date | 2001-03-29 | |
| dc.date | 2005-06-21 | |
| dc.date.accessioned | 2026-07-07T04:40:49Z | |
| dc.date.available | 2026-07-07T04:40:49Z | |
| dc.description | 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 the second symmetric power $C^{(2)}$ of $C$. More precisely, given a pencil $g^1_d$ of degree $d$ on $C$, let $X$ be the curve parametrizing pairs of points in divisors of $g^1_d$ (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$H^0 (g^1_5) = 3$ and $C$ has genus 4. | |
| dc.description | amslatex, 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0103204 | |
| dc.identifier | http://arxiv.org/abs/math/0103204 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61162 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary 14K12, 14C25; Secondary 14B10, 14H40 | |
| dc.title | Deforming curves in jacobians to non-jacobians I: curves in $C^{(2)}$ | |
| dc.type | text |