Algebraic Geometry Seminar
Christian Schnell
Ohio State University
On the canonical extension of a local system
Abstract: In any family of projective varieties, the integral cohomology groups of the smooth fibers
form a local system over the base $B$. In general, this local system is defined only over an
open subset of $B$, because some fibers may be singular, and its behavior near the ``boundary''
contains information about the original family.
Associated to the local system, there is also a vector bundle with a flat connection. In 1970,
Deligne showed in a more general setting how to construct a ``canonical extension'' for this
type of bundle, using the monodromy of the local system, and his construction has since
played a role in Hodge theory. In the talk, we answer the natural question of what happens
to the local system itself at the boundary.
Thursday October 11, 2007 at 4:00 PM in SEO 636