Geometry and cohomology of Khovanov-Springer varieties

TL;DR

This paper provides a new proof of the cohomology ring structure of Khovanov-Springer varieties, linking it to geometric, combinatorial, and algebraic phenomena, enhancing understanding of their mathematical properties.

Contribution

It introduces a novel proof of the cohomology ring structure of Khovanov-Springer varieties and explores its connections to various mathematical phenomena.

Findings

New proof of the cohomology ring structure of X(n)

Connections established between cohomology and geometric, combinatorial, algebraic phenomena

Enhanced understanding of the properties of Khovanov-Springer varieties

Abstract

The Khovanov-Springer variety X(n) is a certain subvariety of the variety of flags of length 2n, which has been studied from various different points of view. We give a new proof of the ring structure of the cohomology of X(n) and relate it to some interesting geometric, combinatorial and algebraic phenomena.