Problems and Progress: A survey on fat points in P

This paper, which expands on a talk given at the International Workshop on Fat Points, February 9-12, 2000, in Naples, Italy, surveys problems and progress on certain problems involving numerical characters for ideals I(Z) defining fat points subschemes Z = m1p1 + · · ·+ mnpn ⊂ P 2 for general points pi. In addition to presenting some new results, a collection of MACAULAY 2 scripts for computing actual or conjectured values of (or bounds on) these characters is included. One such script, findres, for example, computes 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 Gröbner basis calculation, it is much faster than routines that do.