A software package for Mori dream spaces

DOI10.1112/S1461157015000212zbMath1348.14002arXiv1409.6929OpenAlexW3098153801MaRDI QIDQ3449790

Simon Keicher, Hausen, Jürgen

Publication date: 5 November 2015

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.6929

zbMATH Keywords

computer algebra systemMori dream spaceCox ring

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Computational aspects of algebraic surfaces (14Q10) Computational aspects of higher-dimensional varieties (14Q15) Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30) Divisors, linear systems, invertible sheaves (14C20) Software, source code, etc. for problems pertaining to algebraic geometry (14-04)

Related Items (15)

On smooth Fano fourfolds of Picard number two ⋮ Canonical threefold singularities with a torus action of complexity one and \(k\)-empty polytopes ⋮ Iteration of Cox rings of klt singularities ⋮ Algorithms for embedded monoids and base point free problems ⋮ Cox rings over nonclosed fields ⋮ Log terminal singularities, platonic tuples and iteration of Cox rings ⋮ A software package to compute automorphisms of graded algebras ⋮ Toric varieties and Gröbner bases: the complete \(\mathbb{Q}\)-factorial case ⋮ Computing resolutions of quotient singularities ⋮ On Mori chamber and stable base locus decompositions ⋮ MDSpackage ⋮ Embedding non-projective Mori dream space ⋮ ON TORUS ACTIONS OF HIGHER COMPLEXITY ⋮ Cox rings of cubic surfaces and Fano threefolds ⋮ On Gorenstein Fano threefolds with an action of a two-dimensional torus

Uses Software

• Magma
• Maple
• polymake
• Convex
• toric
• TorDiv
• ToricVarieties
• polymake_toric

Cites Work

• A Lefschetz hyperplane theorem for Mori dream spaces
• Mori dream spaces
• The Magma algebra system. I: The user language
• A new linear quotient of \(\mathbf C^4\) admitting a symplectic resolution.
• Hypersurfaces in Mori dream spaces
• Computing with toric varieties
• Cox rings and combinatorics
• Computing Cox rings
• Existence of minimal models for varieties of log general type
• COMPUTING THE GIT-FAN
• Singular del Pezzo surfaces whose universal torsors are hypersurfaces
• A Database of Polarized K3 Surfaces
• Mori dream spaces and GIT.

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