Computing Cox rings

DOI10.1090/mcom/2989zbMath1332.14060arXiv1305.4343OpenAlexW1797309881MaRDI QIDQ3450046

Antonio Laface, Simon Keicher, Hausen, Jürgen

Publication date: 2 November 2015

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

Full work available at URL: https://arxiv.org/abs/1305.4343

zbMATH Keywords

Cox ringsGorenstein log delPezzo surfaceMori dream

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Group actions on varieties or schemes (quotients) (14L30) Computational aspects of algebraic surfaces (14Q10) Computational aspects of higher-dimensional varieties (14Q15) Divisors, linear systems, invertible sheaves (14C20)

Related Items

A software package for Mori dream spaces ⋮ Spherical blow-ups of Grassmannians and Mori dream spaces ⋮ Iteration of Cox rings of klt singularities ⋮ Crepant Resolutions of 3-Dimensional Quotient Singularities via Cox Rings ⋮ On base loci of higher fundamental forms of toric varieties ⋮ Computing resolutions of quotient singularities ⋮ On blowing up the weighted projective plane ⋮ Cox ring of the generic fiber ⋮ Embedding non-projective Mori dream space ⋮ ON TORUS ACTIONS OF HIGHER COMPLEXITY ⋮ Computing automorphisms of Mori dream spaces

Uses Software

• Macaulay2
• Magma
• Maple
• SINGULAR

Cites Work

• On images of Mori dream spaces
• Blow-ups of \(\mathbb{P}^{n-3}\) at \(n\) points and spinor varieties
• Equations for Chow and Hilbert quotients
• On Chow quotients of torus actions
• Sagbi bases of Cox-Nagata rings
• Mori dream spaces
• The Cox ring of an algebraic variety with torus action
• On the factoriality of Cox rings
• Algebraic surfaces with k*-action
• The Magma algebra system. I: The user language
• Homogeneous coordinates for algebraic varieties.
• Factorially graded rings and Cox rings
• Lifting and recombination techniques for absolute factorization
• Gröbner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces
• Del Pezzo and \(K3\) surfaces
• Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
• Cox rings of extremal rational elliptic surfaces
• Cox Rings
• Hilbert's 14th problem and Cox rings
• A Singular Introduction to Commutative Algebra
• Cox rings and combinatorics II
• On Manin's conjecture for a certain singular cubic surface
• Singular del Pezzo surfaces whose universal torsors are hypersurfaces
• Three lectures on Cox rings
• Introduction to the Mori program
• Mori dream spaces and GIT.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Computing Cox rings