Decomposition theorem and torus actions of complexity one

TL;DR

This paper presents an algorithm to compute intersection cohomology Betti numbers for complete normal algebraic varieties with a torus action of complexity one, advancing the understanding of their topological invariants.

Contribution

It introduces a novel algorithmic approach to calculate intersection cohomology Betti numbers specifically for varieties with complexity one torus actions.

Findings

Successfully computes Betti numbers for a broad class of varieties.

Provides a new computational tool for algebraic geometry.

Enhances understanding of topological invariants in torus actions.

Abstract

We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one.