On the topology of rational T-varieties of complexity one

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.

arXiv commentMajor update. In particular, Section 4 was removed and will be uploaded in a new paper entitled "Fundamental group of log terminal T-varieties"