Abel maps of Gorenstein curves
Algebraic Geometry
2007-12-11 v1
Abstract
For a Gorenstein curve X and a nonsingular point P of X, we construct Abel maps A from X to J_X^1 and A_P from X to J_X^0, where J_X^i is the moduli scheme for simple, torsion-free, rank-1 sheaves on X of degree i. The image curves of A and A_P are shown to have the same arithmetic genus of X. Also, A and A_P are shown to be embeddings away from rational subcurves L of X meeting the closure of X-L in separating nodes. Finally, we establish a connection with Seshadri's moduli scheme U_X(1) for semistable, torsion-free, rank-1 sheaves on X, obtaining an embedding of A(X) into U_X(1).
Cite
@article{arxiv.0712.1457,
title = {Abel maps of Gorenstein curves},
author = {Lucia Caporaso and Juliana Coelho and Eduardo Esteves},
journal= {arXiv preprint arXiv:0712.1457},
year = {2007}
}