Bulletin of the Belgian Mathematical Society - Simon Stevin

Stable Postulation and Stable Ideal Generation: Conjectures for Fat Points in the Plane

Alessandro Gimigliano, Brian Harbourne, and Monica Idà

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It is an open problem to determine the Hilbert function and graded Betti numbers for the ideal of a fat point subscheme supported at general points of the projective plane. In fact, there is not yet even a general explicit conjecture for the graded Betti numbers. Here we formulate explicit asymptotic conjectures for both problems. We work over an algebraically closed field $K$ of arbitrary characteristic.

Article information

Bull. Belg. Math. Soc. Simon Stevin Volume 16, Number 5 (2009), 853-860.

First available in Project Euclid: 9 December 2009

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Zentralblatt MATH identifier

Mathematical Reviews number (MathSciNet)

Primary: 14C20: Divisors, linear systems, invertible sheaves 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Secondary: 14J26: Rational and ruled surfaces 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]

Hilbert functions graded Betti numbers fat points splitting types


Gimigliano, Alessandro; Harbourne, Brian; Idà, Monica. Stable Postulation and Stable Ideal Generation: Conjectures for Fat Points in the Plane. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 5, 853--860. http://projecteuclid.org/euclid.bbms/1260369403.

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