Davesh Maulik : Generic and special behavior in families of algebraic varieties

Posted by Emily Dumas , part of the Departmental Colloquium.

At

Feb. 18, 2011, 3 p.m.

In

SEO 636

Abstract

Given a family of complex algebraic varieties, there are different ways of making rigorous the notion of a generic member of the family. In most situations, it is easy to see that these approaches lead to the same behavior. However, for small algebraically closed fields, (e.g. the field of algebraic numbers) this distinction is more subtle, due to the countability of the field. In this talk, we give examples of geometric questions where these issues arise and some different techniques for handling them, when possible. As a special case, we will discuss the behavior of Picard groups in families, following ideas of Y. André, and joint work with B. Poonen.