On the minimal free resolution for fat point schemes of multiplicity at most 3 in P^2

Details On the minimal free resolution for fat point schemes of multiplicity at most 3 in P^2 On the minimal free resolution for fat point schemes of multiplicity at most 3 in P^2

2007-10-08

arxiv.org/abs/0710.1588v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

Let Z be a fat point scheme in P^2 supported on general points. Here we prove
that if the multiplicities are at most 3 and the length of Z is sufficiently
high then the number of generators of the homogeneous ideal I_Z in each degree
is as small as numerically possible. Since it is known that Z has maximal
Hilbert function, this implies that Z has the expected minimal free resolution.

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