Algebraic Geometry Seminar
Jesse Kass
Harvard University
Riemann Singularity Theorems for Singular Curves
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.
Friday November 7, 2008 at 4:30 PM in SEO 636