MDSpackage

A software package for Mori dream spaces. 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.


References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Braun, Lukas; Hättig, Daniel: Canonical threefold singularities with a torus action of complexity one and (k)-empty polytopes (2020)
  2. Laface, Antonio; Massarenti, Alex; Rischter, Rick: On Mori chamber and stable base locus decompositions (2020)
  3. Rossi, Michele: Embedding non-projective Mori dream space (2020)
  4. Rossi, Michele; Terracini, Lea: Toric varieties and Gröbner bases: the complete (\mathbbQ)-factorial case (2020)
  5. Hausen, Jürgen; Hische, Christoff; Wrobel, Milena: On torus actions of higher complexity (2019)
  6. Arzhantsev, Ivan; Braun, Lukas; Hausen, Jürgen; Wrobel, Milena: Log terminal singularities, platonic tuples and iteration of Cox rings (2018)
  7. Fahrner, Anne: Algorithms for embedded monoids and base point free problems (2018)
  8. Donten-Bury, Maria; Keicher, Simon: Computing resolutions of quotient singularities (2017)
  9. Donten-Bury, Maria; Wiśniewski, Jarosław A.: On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32 (2017)
  10. Bechtold, Benjamin; Hausen, Jürgen; Huggenberger, Elaine; Nicolussi, Michele: On terminal Fano 3-folds with 2-torus action (2016)
  11. Derenthal, Ulrich; Hausen, Jürgen; Heim, Armand; Keicher, Simon; Laface, Antonio: Cox rings of cubic surfaces and Fano threefolds (2015)
  12. Hausen, Jürgen; Keicher, Simon: A software package for Mori dream spaces (2015)
  13. Juergen Hausen, Simon Keicher: A software package for Mori dream spaces (2014) arXiv