A software package for Mori dream spaces

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/Wiśniewski.

11 pages, minor changes, to appear in LMS Journal of Computation and Mathematics

References in corpus (1)

• On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32

Cited by in corpus (10)

• Log terminal singularities, platonic tuples and iteration of Cox rings
• On torus actions of higher complexity
• On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32
• Iteration of Cox rings of klt singularities
• Cox rings over nonclosed fields
• Embedding non-projective Mori Dream Spaces
• All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces
• A software package to compute automorphisms of graded algebras
• Étale coverings in codimension 1 with applications to Mori Dream Spaces
• Toric varieties and Gröbner bases: the complete Q-factorial case