Equivariant Chow ring and Chern classes of wonderful symmetric varieties of minimal rank

TL;DR

This paper computes the equivariant Chow ring and Chern classes of the tangent bundle for wonderful symmetric varieties of minimal rank, providing explicit formulas and decompositions into line bundles.

Contribution

It introduces a method to describe the equivariant Chow ring via restriction to a toric variety and derives explicit Chern class formulas for tangent bundles and their logarithmic analogues.

Findings

Explicit description of the equivariant Chow ring via restriction to a toric variety

Decomposition of tangent bundle restrictions into line bundles

Closed formulas for equivariant Chern classes

Abstract

We describe the equivariant Chow ring of the wonderful compactification $X$ of a symmetric space of minimal rank, via restriction to the associated toric variety $Y$. Also, we show that the restrictions to $Y$ of the tangent bundle $T_X$ and its logarithmic analogue $S_X$ decompose into a direct sum of line bundles. This yields closed formulae for the equivariant Chern classes of $T_X$ and $S_X$, and, in turn, for the Chern classes of reductive groups considered by Kiritchenko.