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 suggest a general formula for the multiplicity of the theta divisor of a singular, integral curve at a point and present some evidence that this formula should hold. Our results give a partial answer to a question posed by Lucia Caporaso in a recent paper.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1143-1165
Launched on MUSE
2012-09-22
Open Access
No
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