The minimal free resolution for the first infinitesimal neighborhoods of \(n\) general points in the plane

DOI10.1006/jabr.1998.7772zbMath0943.13008OpenAlexW1972330277MaRDI QIDQ1305058

Monica Idà

Publication date: 7 June 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7772

zbMATH Keywords

Hilbert functionminimal free resolutionfat pointsminimal resolution conjectureHorace methodfirst infinitesimal neighborhood

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Linkage, complete intersections and determinantal ideals (13C40) Syzygies, resolutions, complexes and commutative rings (13D02) Commutative rings and modules of finite generation or presentation; number of generators (13E15)

Related Items (10)

The ideal resolution for generic 3-fat points in \(\mathbb P^2\). ⋮ Good failures for fat points in P² ⋮ The symbolic defect of an ideal ⋮ 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 the minimal free resolution for fat point schemes of multiplicity at most 3 in \(\mathbb P ^2\) ⋮ 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 ⋮ Regina Lectures on Fat Points ⋮ Resolutions of ideals of quasiuniform fat point subschemes of 𝐏²

Cites Work

• The ideal of forms vanishing at a finite set of points in \({\mathbb{P}}^ n\)
• La methode d'Horace pour l'interpolation à plusieurs variables
• The blowing up Horace method: Application to interpolation in degree four
• The minimal resolution conjecture
• Generators for the homogeneous ideal of s general points in \({\mathbb{P}}_ 3\)
• The minimal free resolution of the homogeneous ideal of \(s\) general points in \(\mathbb{P}^ 4\)
• The ideal generation problem for fat points
• Betti numbers of points in projective space
• On the resolution of points in generic position
• Fat points on a conic
• On the homogeneous ideal of the generic union of lines in 3.
• Lectures on Curves on an Algebraic Surface. (AM-59)
• The minimal resolution of the ideal of a general arrangement of a big number of points in \(\mathbb{P}^ n\)
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