Algebraic Geometry Seminar
Christian Schnell
UIC
Residues and $D$-modules
Abstract: Let $X$ be a smooth complex projective variety of dimension $n$. Results by P. Griffiths and M. Green describe the vanishing
cohomology of a sufficiently ample and $\textit{smooth}$ hypersurface $Y \subseteq X$ in terms of residues of $n$-forms on $X$ with
poles along $Y$. In the talk, I will present a generalization of this to all sufficiently ample hypersurfaces, using filtered $D$-modules.
I will explain the connection with M. Saito's theory of mixed Hodge modules, and an application of the result to the Hodge problem.
Friday September 19, 2008 at 4:00 PM in SEO 636