Borel subgroups of $\rm{Aut}(\mathbb{A}^n)$

Abstract: Let $X$ be an affine variety. It was recently proved that a connected solvable $G\subseteq \rm{Aut}(X)$ can be decomposed as a semi-direct product $G=T\ltimes U$ where $T$ is an algebraic torus and $U$ is a nested unipotent subgroup. A $\textit{Borel Subgroup of}$ $\rm{Aut}(X)$ is a maximal element of the set of connected solvable subgroups of $\rm{Aut}(X)$. In this talk I will discuss Borel subgroups of $\rm{Aut}(X)$ with a focus on the special case where $X=\mathbb{A}^n$.

This is joint work with Andriy Regeta and Daniel Daigle.

algebraic geometry

Audience: researchers in the discipline

ODTU-Bilkent Algebraic Geometry Seminars