Equivariant Burnside groups and toric varieties

TL;DR

This paper investigates the $G$-equivariant birational properties of toric varieties, focusing on the role of Burnside groups in understanding symmetries and transformations.

Contribution

It introduces the use of equivariant Burnside groups to analyze the birational geometry of toric varieties with finite group actions, providing new tools for this area.

Findings

Development of a framework linking Burnside groups to equivariant birational geometry

New invariants for classifying toric varieties under finite group actions

Insights into the structure of $G$-equivariant birational maps

Abstract

We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.