Divisor class groups of rational trinomial varieties

TL;DR

This paper provides an explicit description of the divisor class groups for rational trinomial varieties and explores their relation to Cox rings and Du Val surfaces, enhancing understanding of their algebraic structure.

Contribution

It offers a novel explicit characterization of divisor class groups for rational trinomial varieties and links Cox ring iterations to Du Val surfaces.

Findings

Explicit divisor class group descriptions for rational trinomial varieties

Connection established between Cox ring iteration and Du Val surfaces

Enhanced understanding of algebraic structure of these varieties

Abstract

We give an explicit description of the divisor class groups of rational trinomial varieties. As an application, we relate the iteration of Cox rings of any rational variety with torus action of complexity one to that of a Du Val surface.