Wonderful varieties with a view towards Poisson geometry

TL;DR

This paper provides an accessible overview of wonderful varieties, their construction, and their connections to Poisson geometry and Lagrangian subalgebras, aimed at readers new to algebraic geometry.

Contribution

It offers an explicit construction of the wonderful compactification of semisimple adjoint groups and explores their links to Poisson structures and Lagrangian subvarieties.

Findings

Explicit construction of wonderful compactification

Connections established between wonderful varieties and Poisson geometry

Survey accessible to non-specialists in algebraic geometry

Abstract

These are expanded lecture notes from the author's minicourse at the 2022 Poisson Geometry Summer School, which took place at the Centre de Recerca Matematica in Barcelona, Spain. After giving a general introduction to wonderful varieties, and an explicit construction of the wonderful compactification of a semisimple adjoint group, we outline several connections to Poisson geometry and to varieties of Lagrangian subalgebras. This survey is intended to be accessible to readers without an extensive background in algebraic geometry.