Greg Taylor : Groups of birational transformations of algebraic surfaces

Posted by Gregory Taylor , part of the Graduate Algebraic Geometry Seminar.

At

Jan. 22, 2020, 4 p.m.

In

512 SEO

Abstract

The collection of birational self-maps of an algebraic variety X forms a group Bir(X). When X is a surface, this group acts on an infinite hyperbolic space, constructed via divisors on blowups of the surface. In this talk, we introduce this construction and use it to understand Bir(X). Time permitting, we will discuss very recent work of Lonjou and Urech on Bir(X) for higher dimensional X. The main source for this talk is the paper "Sur les groupes de transformations birationnelles des surfaces" by Serge Cantat.