A Riemann singularity theorem for integral curves

• Autores: Sebastian Casalaina-Martin, Jesse Leo Kass
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 134, Nº 5, 2012, págs. 1143-1165
• Idioma: inglés
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• Resumen

  • 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.