Polarized Complexity-One T-Varieties

TL;DR

This paper provides a combinatorial description of polarized complexity-one T-varieties using divisorial polytopes, enabling the reading of geometric properties and explicit generator construction.

Contribution

It introduces a new combinatorial framework for polarized complexity-one T-varieties and compares it with existing descriptions.

Findings

Divisorial polytopes encode geometric properties of T-varieties.

Method to explicitly find generators of affine complexity-one T-varieties.

Comparison with other descriptions enhances understanding of T-varieties.

Abstract

We describe polarized complexity-one T-varieties combinatorially in terms of so-called divisorial polytopes, and show how geometric properties of such a variety can be read off the corresponding divisorial polytope. We compare our description with other possible descriptions of polarized complexity-one T-varieties. We also describe how to explicitly find generators of affine complexity-one T-varieties.