Jesse Kass : Riemann Singularity Theorems for Singular Curves

Posted by , part of the Algebraic Geometry Seminar.

At

Nov. 7, 2008, 4:30 p.m.

In

SEO 636

Abstract

A classical result of Riemann computes the multiplicity of the theta divisor of a non-singular curve at a point. If $x$ is a point of $\Theta$ that corresponds to a line bundle $L$, then the Riemann singularity theorem states that: $mult_{x}(\Theta) = h^{1}(X,L)$. I will talk about extending this theorem to singular integral curves. In particular, I prove a direct generalization of Riemann's theorem to nodal integral curves. This result yields a partial answer to a question of Lucia Caporaso. This work is joint with Sebastian (Yano) Casalaina-Martin.