Free resolutions of fat point ideals on \(\mathbb{P}^2\)

DOI10.1016/S0022-4049(96)00126-0zbMath0901.14030arXivalg-geom/9509002OpenAlexW3105040771WikidataQ127517450 ScholiaQ127517450MaRDI QIDQ1380053

Brian Harbourne

Publication date: 26 November 1998

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9509002

zbMATH Keywords

infinitely near pointseffective divisor classesfat point subscheme

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Computational aspects and applications of commutative rings (13P99) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02) Divisors, linear systems, invertible sheaves (14C20)

Related Items

The symbolic generic initial system of almost linear point configurations in \(\mathbb P^2\) ⋮ Rational normal curves and Hadamard products ⋮ Symbolic powers of planar point configurations ⋮ Harbourne–Hirschowitz surfaces whose anticanonical divisors consist only of three irreducible components ⋮ Algebraic geometric codes on anticanonical surfaces ⋮ The effective monoids of some blow-ups of Hirzebruch surfaces ⋮ Platonic Harbourne-Hirschowitz rational surfaces ⋮ Platonic Surfaces ⋮ ON THE BETTI NUMBERS OF THREE FAT POINTS IN ℙ 1 × ℙ 1 ⋮ On base loci of higher fundamental forms of toric varieties ⋮ The resurgence of ideals of points and the containment problem ⋮ Resolutions of ideals of any six fat points in \(\mathbb{P}^{2}\) ⋮ Configuration types and cubic surfaces ⋮ Maps of linear systems on blow-ups of the projective plane. ⋮ On the existence of plane curves with imposed multiple points ⋮ On bounding the number of generators for fat point ideals on the projective plane ⋮ On Nagata's conjecture ⋮ On the finite generation of the effective monoid of rational surfaces ⋮ Fat points schemes on a smooth quadric ⋮ Resolutions of fat points ideals involving eight general point of \(\mathbb{P}^2\) ⋮ Betti numbers for fat point ideals in the plane: A geometric approach ⋮ The minimal resolutions of double points in \(\mathbb {P}^1 \times \mathbb P^{1}\) with ACM support ⋮ Homaloidal nets and ideals of fat points I ⋮ Lower semi-continuity of the Waldschmidt constants ⋮ Classifying Hilbert functions of fat point subschemes in \(\mathbb{P}^2\) ⋮ Resolutions of ideals of fat points with support in a hyperplane ⋮ Regina Lectures on Fat Points ⋮ Resolutions of ideals of quasiuniform fat point subschemes of 𝐏²

Cites Work

• Blowings-up of \({\mathbb{P}}^ 2\) and their blowings-down
• The minimal resolution conjecture
• Birational morphisms of rational surfaces
• Anticanonical Rational Surfaces
• Some Numerical Criteria for Contractability of Curves on Algebraic Surfaces
• Complete Linear Systems on Rational Surfaces
• Fat points on a conic
• Une conjecture pour la cohomologie des diviseurs sur les surfaces rationelles génériques.
• Rational surfaces with $K^2>0$
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Free resolutions of fat point ideals on \(\mathbb{P}^2\)