A software package for Mori dream spaces

TL;DR

This paper introduces a software package designed to explicitly handle Mori dream spaces, including a Cox ring database, enabling concrete computations and applications in algebraic geometry.

Contribution

It provides the first dedicated software tool for Mori dream spaces, facilitating explicit calculations and analysis in the field.

Findings

Successfully computed Cox rings for specific Mori dream spaces.

Demonstrated the software's use with examples involving symplectic resolutions.

Established a database of Cox rings for algebraic varieties.

Abstract

Mori dream spaces form a large example class of algebraic varieties, comprising the well known toric varieties. We provide a first software package for the explicit treatment of Mori dream spaces and demonstrate its use by presenting basic sample computations. The software package is accompanied by a Cox ring database which delivers defining data for Cox rings and Mori dream spaces in a suitable format. As an application of the package, we determine the common Cox ring for the symplectic resolutions of a certain quotient singularity investigated by Bellamy/Schedler and Donten-Bury/Wi\'sniewski.