English

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

R2 v1 2026-06-24T09:05:31.020Z