Resolutions of fat points ideals involving eight general point of \(\mathbb{P}^2\)

DOI10.1006/jabr.2001.8931zbMath1033.14031OpenAlexW1989164877MaRDI QIDQ5952415

Stephanie Fitchett, Brian Harbourne, Sandeep H. Holay

Publication date: 29 March 2004

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

Full work available at URL: https://doi.org/10.1006/jabr.2001.8931

zbMATH Keywords

algorithmHilbert functionrational surfacefat pointsdivisor class groupgraded Betti numbersgraded free resolution

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40)

Related Items (17)

The asymptotic behaviour of symbolic generic initial systems of generic points ⋮ Homaloidal nets and ideals of fat points II: Subhomaloidal nets ⋮ The ideal resolution for generic 3-fat points in \(\mathbb P^2\). ⋮ 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 ⋮ Configuration types and cubic surfaces ⋮ On bounding the number of generators for fat point ideals on the projective plane ⋮ 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 ⋮ On the finite generation of the effective monoid of rational surfaces ⋮ On the first infinitesimal neighborhood of a linear configuration of points in \(\mathbb P^2\) ⋮ 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 ⋮ 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
• Linear systems of plane curves through fixed fat points of \(\mathbb{P}^ 2\)
• The \(d\)-very ampleness on a projective surface in positive characteristic
• Birational morphisms of rational surfaces
• Free resolutions of fat point ideals on \(\mathbb{P}^2\)
• The ideal generation problem for fat points
• Anticanonical Rational Surfaces
• On rational surfaces, II
• Complete Linear Systems on Rational Surfaces
• An Algorithm for Fat Points on P²
• Rational surfaces with $K^2>0$
• Varieties Defined by Quadratic Equations
• Maps of linear systems on blow-ups of the projective plane.
• On bounding the number of generators for fat point ideals on the projective plane
• Unnamed Item

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