## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

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

Alessandro Gimigliano, Brian Harbourne, and Monica Idà

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 9 December 2009

**Permanent link to this document**

http://projecteuclid.org/euclid.bbms/1260369403

**Mathematical Reviews number (MathSciNet)**

MR2574365

**Zentralblatt MATH identifier**

05658087

**Subjects**

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]

**Keywords**

Hilbert functions graded Betti numbers fat points splitting types

#### Citation

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.