Cohomology of Spaltenstein varieties

TL;DR

This paper provides a new algebraic presentation for the cohomology of Spaltenstein varieties, extending known results from Springer fibers to a broader class of partial flag varieties.

Contribution

It generalizes the cohomology algebra description from Springer fibers to all partial flags annihilated by a fixed nilpotent matrix.

Findings

Presented a new algebraic description of cohomology for Spaltenstein varieties.

Extended Springer fiber cohomology results to partial flag varieties.

Provides tools for further geometric and algebraic analysis of these varieties.

Abstract

We give a presentation for the cohomology algebra of the Spaltenstein variety of all partial flags annihilated by a fixed nilpotent matrix, generalizing the description of the cohomology algebra of the Springer fiber found by De Concini, Procesi and Tanisaki.