Explicit Decomposition Theorem for special Schubert varieties

TL;DR

This paper provides a concise proof of the Decomposition Theorem for a class of special Schubert varieties, along with explicit descriptions of perverse sheaves and a simplified proof of the Relative Hard Lefschetz Theorem.

Contribution

It offers a new, self-contained proof of the Decomposition Theorem and explicit descriptions of perverse sheaves for special Schubert varieties.

Findings

Proof of the Decomposition Theorem for non-small resolutions

Explicit description of perverse cohomology sheaves

Simplified proof of the Relative Hard Lefschetz Theorem

Abstract

We give a short and self-contained proof of the Decomposition Theorem for the non-small resolution of a Special Schubert variety. We also provide an explicit description of the perverse cohomology sheaves. As a by-product of our approach, we obtain a simple proof of the Relative Hard Lefschetz Theorem.