Degree-2 Abel maps and hyperelleptic curves
Algebraic Geometry
2022-01-28 v1
Abstract
In this paper we resolve the degree-2 Abel map for nodal curves. Our results are based on a previous work of the authors reducing the problem of the resolution of the Abel map to a combinatorial problem via tropical geometry. As an application, we characterize when the (symmetrized) degree-2 Abel map is not injective, a property that, for a smooth curve, is equivalent to the curve being hyperelliptic.
Keywords
Cite
@article{arxiv.2201.11535,
title = {Degree-2 Abel maps and hyperelleptic curves},
author = {Alex Abreu and Sally Andria and Marco Pacini},
journal= {arXiv preprint arXiv:2201.11535},
year = {2022}
}
Comments
19 pages, 10 figures