Christian Schnell : Residues and $D$-modules

Posted by , part of the Algebraic Geometry Seminar.

At

Sept. 19, 2008, 4 p.m.

In

SEO 636

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.