On the topology of rational T-varieties of complexity one

TL;DR

This paper extends classical topological results from toric varieties to rational T-varieties of complexity one, providing formulas for Hodge-Deligne polynomials, cohomology, and Chow rings using divisorial fans.

Contribution

It introduces a generalized framework for analyzing the topology of T-varieties of complexity one, including explicit descriptions of their cohomological invariants.

Findings

Hodge-Deligne polynomial formulas for smooth cases

Cohomology ring descriptions for contraction-free T-varieties

Chow ring structures derived for these varieties

Abstract

We generalize classical results about the topology of toric varieties to the case of projective Q-factorial T-varieties of complexity one using the language of divisorial fans. We describe the Hodge-Deligne polynomial in the smooth case, the cohomology ring and the Chow ring in the contraction-free case.