# Moscow Mathematical Journal

Volume 20, Issue 2, April–June 2020  pp. 405–422.

On the Topology of Rational $\mathbb{T}$-Varieties of Complexity One

Authors:  Antonio Laface (1), Alvaro Liendo (2), and Joaquín Moraga (3)
Author institution:(1) Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
(2) Instituto de Matemática y Física, Universidad de Talca, Casilla 721, Talca, Chile
(3) Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112

Summary:

We generalize classical results about the topology of toric varieties to the case of projective $\mathbb{Q}$-factorial $\mathbb{T}$-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.

2010 Math. Subj. Class. 14C15, 14L30, 14M25.

Keywords: T-varieties, Hodge–Deligne polynomials, torus actions, Chow rings, topology of T-varieties.