The cone of curves and the Cox ring of rational surfaces given by divisorial valuations

DOI10.1016/j.aim.2015.12.015zbMath1431.13006arXiv1402.4257OpenAlexW1567543332MaRDI QIDQ908090

Francisco Monserrat, Carlos Galindo Pastor

Publication date: 2 February 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.4257

zbMATH Keywords

rational surfacesCox ringcone of curvesplane divisorial valuation

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Valuations and their generalizations for commutative rings (13A18) Divisors, linear systems, invertible sheaves (14C20)

Related Items

Minimal plane valuations ⋮ The effective monoids of some blow-ups of Hirzebruch surfaces ⋮ Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces ⋮ On the effective, nef, and semi-ample monoids of blowups of Hirzebruch surfaces at collinear points ⋮ Platonic Harbourne-Hirschowitz rational surfaces ⋮ Platonic Surfaces ⋮ Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces ⋮ Rational surfaces with finitely generated Cox rings and very high Picard numbers ⋮ Newton-Okounkov bodies of exceptional curve valuations ⋮ Discrete equivalence of non-positive at infinity plane valuations ⋮ On the computation of Darboux first integrals of a class of planar polynomial vector fields

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