Characterizing Varieties Using Birational Transformations
Organizers
Speaker
Louis Esser
Time
Thursday, September 17, 2026 10:00 AM - 11:00 AM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Given a mathematical object X in a category C, it is natural to ask whether the group of symmetries of X determines X, up to equivalence in C. The answer to this question is known to be positive in several natural categories of spaces, including topological and smooth manifolds. In this talk, we consider the analogous questions for complex algebraic varieties. While algebraic maps are too rigid for there to be "enough" symmetries in general, we prove that for a variety X carrying an action by a nontrivial connected linear algebraic group, the group of birational transformations Bir(X) determines X, up to birational equivalence and field automorphisms. In contrast, we show that Bir(X) can never determine X unless X is covered by rational curves. This talk is based on joint work with N. Chen, A. Regeta, C. Urech, and I. van Santen.