Higher cohomology vanishing of line bundles on generalized Springer's resolution

TL;DR

This paper proves a conjecture related to higher cohomology vanishing of line bundles on generalized Springer resolutions, leading to non-negativity results for multivariable Kostka functions.

Contribution

It provides a proof of a conjecture by Finkelberg and Ionov, establishing higher cohomology vanishing and non-negativity of certain Kostka function coefficients.

Findings

Higher cohomology of line bundles vanishes on generalized Springer resolutions

Coefficients of multivariable Kostka functions are non-negative

Confirms conjecture by Finkelberg and Ionov

Abstract

We give a proof of a conjecture raised by Michael Finkelberg and Andrei Ionov. As a corollary, the coefficients of multivariable version of Kostka functions introduced by Finkelberg and Ionov are non-negative.