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A software package for Mori dream spaces

Part of: Computational aspects in algebraic geometry

Published online by Cambridge University Press:  01 November 2015

Jürgen Hausen  and
Simon Keicher
Jürgen Hausen
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany email juergen.hausen@uni-tuebingen.de
Simon Keicher
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany email keicher@mail.mathematik.uni-tuebingen.de

Abstract

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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.

MSC classification

Primary: 14Q10: Surfaces, hypersurfaces 14Q15: Higher-dimensional varieties
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 647 - 659
Copyright
© The Author(s) 2015 

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