Computing limit linear series with infinitesimal methods

DOI10.5802/aif.2319zbMath1134.14020arXivmath/0407143OpenAlexW2949231926MaRDI QIDQ2466306

Laurent Evain

Publication date: 14 January 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407143

zbMATH Keywords

singularitiescurveHilbert functionfat pointnagata

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Divisors, linear systems, invertible sheaves (14C20) Singularities of curves, local rings (14H20) Infinitesimal methods in algebraic geometry (14B10) Formal neighborhoods in algebraic geometry (14B20)

Related Items (13)

Algebraic Geometry, Commutative Algebra and Combinatorics: Interactions and Open Problems ⋮ Homogeneous interpolation on ten points ⋮ On the secant varieties of tangential varieties ⋮ Tropical approach to Nagata's conjecture in positive characteristic ⋮ All fat point subschemes in \(\mathbb{P}^2\) with the Waldschmidt constant less than 5/2 ⋮ The resurgence of ideals of points and the containment problem ⋮ Resolutions of ideals of any six fat points in \(\mathbb{P}^{2}\) ⋮ The role of the cotangent bundle in resolving ideals of fat points in the plane ⋮ Interpolation on surfaces in ℙ³ ⋮ On the minimal free resolution for fat point schemes of multiplicity at most 3 in \(\mathbb P ^2\) ⋮ Combinatorial bounds on Hilbert functions of fat points in projective space ⋮ Betti numbers for fat point ideals in the plane: A geometric approach ⋮ Unnamed Item

Cites Work

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• La methode d'Horace pour l'interpolation à plusieurs variables
• Infinitely near imposed singularities and singularities of polar curves
• Symplectic packings and algebraic geometry
• An asymptotic vanishing theorem for generic unions of multiple points
• On the symmetric product of a curve with general moduli
• Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
• On rational surfaces, II
• Degenerations of Planar Linear Systems
• Calculs de dimensions de systèmes linéaires de courbes planes par collisions de gros points
• Ample line bundles on smooth surfaces.

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