arXiv 0907.02122009-07math.AG

A Riemann singularity theorem for integral curves

Sebastian Casalaina-Martin, Jesse Leo Kass

备注：: 23 pages, AMS Latex, improved exposition, to appear in the Amer. J. Math
发表信息：: Amer. J. Math. 134 (2012), no. 5, 1143--1165

英文摘要：

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.

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