Resolutions of ideals of quasiuniform fat point subschemes of 𝐏²

DOI10.1090/S0002-9947-02-03124-0zbMath1028.14020arXivmath/9906130OpenAlexW1500944529MaRDI QIDQ4779884

Stephanie Fitchett, Brian Harbourne, Sandeep H. Holay

Publication date: 28 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9906130

zbMATH Keywords

regularityHilbert functionminimal free resolutionfat pointssymbolic powersmaximal rankideal generation conjecturequasiuniformity

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Multiplicity theory and related topics (13H15) Syzygies, resolutions, complexes and commutative rings (13D02)

Related Items (16)

An algorithm to bound the regularity and nonemptiness of linear systems in \(\mathbb P^n\) ⋮ Containment results for ideals of various configurations of points in \(\mathbb P^N\) ⋮ 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 ⋮ On Nagata's conjecture ⋮ 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 first infinitesimal neighborhood of a linear configuration of points in \(\mathbb P^2\) ⋮ Fat points schemes on a smooth quadric ⋮ Betti numbers for fat point ideals in the plane: A geometric approach ⋮ Curves having one place at infinity and linear systems on rational surfaces ⋮ Unnamed Item ⋮ Regina Lectures on Fat Points

Cites Work

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• Regularity of linear systems of plane curves
• Monomial ideals and points in projective space
• Standard bases of perfect homogeneous polynomial ideals of height 2
• Minimally generating ideals defining certain tangent cones
• The minimal free resolution for the first infinitesimal neighborhoods of \(n\) general points in the plane
• Free resolutions of fat point ideals on \(\mathbb{P}^2\)
• An asymptotic vanishing theorem for generic unions of multiple points
• The ideal generation problem for fat points
• Anticanonical Rational Surfaces
• On rational surfaces, II
• Fat points on a conic
• Une conjecture pour la cohomologie des diviseurs sur les surfaces rationelles génériques.
• Degenerations of Planar Linear Systems
• Linear systems with multiple base points in ℙ²
• Linear systems of plane curves with base points of equal multiplicity
• An Algorithm for Fat Points on P²
• Ample line bundles on smooth surfaces.
• On the 14-th Problem of Hilbert
• 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
• Resolutions of fat points ideals involving eight general point of \(\mathbb{P}^2\)
• Linear systems of plane curves with imposed multiple points

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