Colloquium
Thursday February 28th, 2019
Time: 4:00 PM - 5:00 PM
Title: o-minimal GAGA
Speaker: Benjamin Bakker, University of Georgia
Location: Math Tower P-131
Abstract:

A complex algebraic variety can be naturally considered as a complex analytic space. Working with the analytic space often has many advantages, as for instance there are many more complex analytic functions than algebraic ones. For this perspective to be useful in algebraic geometry, it is necessary to also go backwards---that is, to characterize when analytic constructions starting with algebraic varieties return algebraic varieties. One powerful answer to this question is provided by Serre's celebrated GAGA theorem. It generalizes an earlier result of Chow asserting that closed complex analytic subspaces of a compact algebraic variety are in fact algebraic. Both of these theorems easily fail for non-compact algebraic varieties.

In this talk I will explain joint work with Y. Brunebarbe and J. Tsimerman which shows that Serre's GAGA theorem extends to the non-compact case if one restricts to analytic structures that are "tame" in a sense made precise by the model-theoretic notion of o-minimality. We will also explain why this result has important applications to Hodge theory.