Equivariant Birational Geometry of Linear Actions

Explore the intricacies of equivariant birational geometry in this 31-minute lecture from the University of Miami. Delve into the Burnside group formalism developed by Kontsevich, Kresch, and Tschinkel as applied to linear actions on projective spaces. Discover new findings in two-dimensional spaces, where the formalism reveals previously unknown non-birational linear and projectively linear actions. Examine the extension of these concepts to three-dimensional spaces, uncovering novel types of non-birational linear actions on P^3 and non-linearizable actions on smooth quadrics. Gain insights into advanced mathematical concepts at the intersection of algebraic geometry and group theory.