Classification of strict wonderful varieties

TL;DR

This paper proves that strict wonderful varieties are classified by spherical systems, confirming Luna's conjecture, and shows they mainly originate from symmetric spaces, nilpotent orbits, or model spaces.

Contribution

It confirms Luna's conjecture for strict wonderful varieties and clarifies their main sources from well-understood geometric families.

Findings

Strict wonderful varieties are classified by spherical systems.

Most strict wonderful varieties derive from symmetric spaces, nilpotent orbits, or model spaces.

The paper consolidates known results to make the classification self-contained.

Abstract

In the setting of strict wonderful varieties we answer positively to Luna's conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits or model spaces. To make the paper self-contained as much as possible, we shall gather some known results on these families and more generally on wonderful varieties.