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.
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