Cox rings and combinatorics

DOI10.1090/S0002-9947-06-03904-3zbMath1117.14009arXivmath/0311105OpenAlexW2145779835MaRDI QIDQ3420268

Florian Berchtold, Hausen, Jürgen

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311105

zbMATH Keywords

Fano varietyCox ring\(A_2\)-maximalitybunched ring

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Rational and unirational varieties (14M20) Computational aspects of higher-dimensional varieties (14Q15) Fano varieties (14J45) Divisors, linear systems, invertible sheaves (14C20) Hypersurfaces and algebraic geometry (14J70)

Related Items

On smooth Fano fourfolds of Picard number two, A software package for Mori dream spaces, ON SMOOTHNESS OF MINIMAL MODELS OF QUOTIENT SINGULARITIES BY FINITE SUBGROUPS OF SL_n(ℂ), A geometric criterion for the finite generation of the Cox rings of projective surfaces, On embeddings of homogeneous spaces with small boundary, Examples of counting curves on surfaces, On Chow quotients of torus actions, Log Fano structures and Cox rings of blow-ups of products of projective spaces, On the effective, nef, and semi-ample monoids of blowups of Hirzebruch surfaces at collinear points, Mori dream spaces as fine moduli of quiver representations, Cox rings of rational complexity-one \(T\)-varieties, Examples of Non-finitely Generated Cox Rings, COMPUTING THE GIT-FAN, On pliability of del Pezzo fibrations and Cox rings, Geometric invariant theory via Cox rings, GIT-equivalence beyond the ample cone, Valuative and geometric characterizations of Cox sheaves, Manin's conjecture for a certain family of intrinsic quadrics, Moduli spaces of curves and Cox rings, The Cox ring of an algebraic variety with torus action, Mori dream stacks, On Intrinsic Quadrics, COX RINGS OF MINIMAL RESOLUTIONS OF SURFACE QUOTIENT SINGULARITIES, Galois actions on analytifications and tropicalizations, A survey on Cox rings, Infinite transitivity on universal torsors, ON TORUS ACTIONS OF HIGHER COMPLEXITY, Cox rings of cubic surfaces and Fano threefolds, Differentials of Cox rings: Jaczewski's theorem revisited

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a conjecture of Cox and Katz
• On linearizing algebraic torus actions
• Singularités rationnelles et quotients par les groupes réductifs. (Rational singularities and quotients by reductive groups)
• A classification of toric varieties with few generators
• Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions
• Über einige Eindeutigkeitssätze für konvexe Körper
• On Hilbert's fourteenth problem for varieties of complexity one.
• Three theorems on existence of good quotients
• Homogeneous coordinates for algebraic varieties.
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• Lifting of morphisms to quotient presentations
• The total coordinate ring of a normal projective variety
• Toward a numerical theory of ampleness
• Affine open subsets of algebraic varieties and ample divisors
• Introduction to Toric Varieties. (AM-131)
• Geometric Invariant Theory
• A combinatorial construction of sets with good quotients by an action of a reductive group
• Introduction to the Mori program
• Polygons with hidden vertices
• Mori dream spaces and GIT.