About the cohomological dimension of certain stratified varieties

TL;DR

This paper establishes an upper bound for the cohomological dimension of the complement of a closed subset in stratified projective varieties, with applications to specific stratifications like Bialynicki-Birula, where the bound is shown to be optimal.

Contribution

It provides a general method to bound cohomological dimensions in stratified projective varieties and demonstrates optimal bounds in particular cases.

Findings

Derived an upper bound for cohomological dimension in stratified varieties

Applied the bound to Bialynicki-Birula stratification, confirming optimality

Extended understanding of cohomological properties in algebraic geometry

Abstract

We determine an upper bound for the cohomological dimension of the complement of a closed subset in a projective variety which possesses an appropriate stratification. We apply the result to several particular cases, including the Bialynicki-Birula stratification; in this latter case, the bound is optimal.