English

A Riemann singularity theorem for integral curves

Algebraic Geometry 2015-03-13 v2

Abstract

We prove results generalizing the classical Riemann Singularity Theorem to the case of integral, singular curves. The main result is a computation of the multiplicity of the theta divisor of an integral, nodal curve at an arbitrary point. We also conjecture a general formula for the multiplicity of points on the theta divisor of a singular integral curve and present some evidence for this conjecture. Our results give a partial answer to a question posed by Lucia Caporaso in a recent paper.

Keywords

Cite

@article{arxiv.0907.0212,
  title  = {A Riemann singularity theorem for integral curves},
  author = {Sebastian Casalaina-Martin and Jesse Leo Kass},
  journal= {arXiv preprint arXiv:0907.0212},
  year   = {2015}
}

Comments

23 pages, AMS Latex, improved exposition, to appear in the Amer. J. Math

R2 v1 2026-06-21T13:20:13.219Z