Hilbert functions of fat point subschemes of the plane: the two-fold way
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Publication:2895430
zbMath1251.14027arXiv1101.5140MaRDI QIDQ2895430
Anthony V. Geramita, Brian Harbourne, Juan C. Migliore
Publication date: 2 July 2012
Abstract: Two approaches for determining Hilbert functions of fat point subschemes of $mathbb P^2$ are demonstrated. A complete determination of the Hilbert functions which occur for 9 double points is given using the first approach, extending results obtained in a previous paper using the second approach. In addition the second approach is used to obtain a complete determination of the Hilbert functions for $ngeq 9$ $m$-multiple points for every $m$ if the points are smooth points of an irreducible plane cubic curve. Additional results are obtained using the first approach for $ngeq 9$ double points when the points lie on an irreducible cubic (but now are not assumed to be smooth points of the cubic).
Full work available at URL: https://arxiv.org/abs/1101.5140
Rational and ruled surfaces (14J26) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Linkage (14M06) Projective techniques in algebraic geometry (14N05) Low codimension problems in algebraic geometry (14M07)
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