Problems and progress: survey on fat points in P2

Details Problems and progress: survey on fat points in P2 Problems and progress: survey on fat points in P2

2001-01-12

arxiv.org/abs/math/0101112v1

Mathematics

Algebraic Geometry

46 pages PlainTeX (includes 23 pages of Macaulay 2 scripts which can be copied and pasted directly into Macaulay)

Scientific paper

This paper surveys certain problems involving numerical characters for ideals I(Z) defining fat points subschemes $Z=m_1p_1+...+m_np_n$ for general points $p_i\in {\bf P}^2$. It also presents some new results, and includes a suite of MACAULAY 2 scripts for computing actual or conjectured values of (or bounds on) these characters. One such script, for example, is findres, which implements an algorithm due to Fitchett, Harbourne and Holay for computing the syzygy modules in a minimal free resolution of the ideal I(Z) for any such Z with n<=8; since findres does not rely on a Gr\"obner basis calculation, it is very fast and can handle very large multiplicities.

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