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.
Citation
Alessandro Gimigliano. Brian Harbourne. Monica Idà. "Stable Postulation and Stable Ideal Generation: Conjectures for Fat Points in the Plane." Bull. Belg. Math. Soc. Simon Stevin 16 (5) 853 - 860, December 2009. https://doi.org/10.36045/bbms/1260369403
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