Birational geometry for nilpotent orbits

TL;DR

This survey reviews the birational geometry of nilpotent orbits, including resolutions, terminalizations, and Poisson deformations, providing a comprehensive overview of current mathematical understanding in this area.

Contribution

It compiles and discusses recent advances in the birational geometry and deformation theory of nilpotent orbit closures, serving as a comprehensive resource.

Findings

Overview of resolutions for nilpotent orbits

Discussion of Q-factorial terminalizations and birational geometry

Analysis of Poisson deformations of orbit closures

Abstract

This is a survey article prepared for the submission to "Handbook of moduli". The following topics are discussed: (i) Basic facts and examples of resolutions for nilpotent orbit (ii) Q-factorial terminalizations of nilpotent orbit closures and related birational geometry (iii) Poisson deformations of nilpotent orbit closures.