The total coordinate ring of a smooth projective surface

DOI10.1016/j.jalgebra.2004.10.004zbMath1108.14007OpenAlexW2048788081MaRDI QIDQ1764831

Francisco Monserrat, Carlos Galindo Pastor

Publication date: 22 February 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.10.004

zbMATH Keywords

algebraic surfacestotal coordinate ring (``Cox ring)

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Minimal model program (Mori theory, extremal rays) (14E30) Divisors, linear systems, invertible sheaves (14C20) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15)

Related Items (12)

A geometric criterion for the finite generation of the Cox rings of projective surfaces ⋮ Algebraic integrability of foliations of the plane ⋮ Minimal plane valuations ⋮ The effective monoids of some blow-ups of Hirzebruch surfaces ⋮ On the effective, nef, and semi-ample monoids of blowups of Hirzebruch surfaces at collinear points ⋮ The cone of curves and the Cox ring of rational surfaces given by divisorial valuations ⋮ Big rational surfaces ⋮ Platonic Surfaces ⋮ Rational surfaces with finitely generated Cox rings and very high Picard numbers ⋮ The cone conjecture for Calabi-Yau pairs in dimension 2 ⋮ Curves having one place at infinity and linear systems on rational surfaces ⋮ Cox rings of rational surfaces and redundant blow-ups

Cites Work

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• Cones of curves and of line bundles ``at infinity
• Anticanonical Rational Surfaces
• Valuations in Function Fields of Surfaces
• On rational surfaces, II
• Holomorphic symmetries
• The Poincaré series associated with finitely many monomial valuations
• The Euler Series of Restricted Chow Varieties
• ON THE CONE OF CURVES AND OF LINE BUNDLES OF A RATIONAL SURFACE
• Mori dream spaces and GIT.
• Some remarks on Chow varieties and Euler-Chow series

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