Departmental Colloquium

Event Information o-minimal GAGA and applications to Hodge theory
16:00 on Wednesday October 24, 2018
17:00 on Wednesday October 24, 2018
BA6183, Bahen Center, 40 St. George St.
Jacob Tsimerman
http://www.math.toronto.edu/~jacobt/
University of Toronto

(joint with B.Bakker and Y.Brunebarbe) One very fruitful way of studying complex algebraic varieties is by forgetting the underlying algebraic structure, and just thinking of them as complex analytic spaces. To this end, it is a natural and fruitful question to ask how much the complex analytic structure remembers. One very prominent result is Chows theorem, stating that any closed analytic subspace of projective space is in fact algebraic. A notable consequence of this result is that a compact complex analytic space admits at most 1 algebraic structure - a result which is false in the non-compact case. This was generalized and extended by Serre in his famous GAGA paper using the language of cohomology.

We will explain how to extend Chow's theorem and its generalization to GAGA to the non-compact case by working with complex analytic structures that are "tame" in the precise sense defined by o-minimality. This leads to some very general "algebraization" theorems, and we give applications to Hodge theory.