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

Alessandro Gimigliano, Brian Harbourne, and Monica Idà
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 16, Number 5 (2009), 853-860.

#### 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.

First Page:
Primary Subjects: 14C20, 13P10
Secondary Subjects: 14J26, 14J60