Points

Macaulay2 package Points - A package for making and studying points in affine and projective spaces. The package has routines for points in affine and projective spaces. The affine code, some of which uses the Buchberger-Moeller algorithm to more quickly compute the ideals of points in affine space, was written by Stillman, Smith and Stromme. The projective code was written separately by Eisenbud and Popescu. The purpose of the projective code was to find as many counterexamples as possible to the minimal resolution conjecture; it was of use in the research for the paper ”Exterior algebra methods for the minimal resolution conjecture”, by David Eisenbud, Sorin Popescu, Frank-Olaf Schreyer and Charles Walter (Duke Mathematical Journal. 112 (2002), no.2, 379-395.) The first few of these counterexamples are: (6,11), (7,12), (8,13), (10,16), where the first integer denotes the ambient dimension and the second the number of points. Examples are known in every projective space of dimension >=6 except for P9. In version 3.0, F. Galetto and J.W. Skelton added code to compute ideals of fat points and projective points using the Buchberger-Moeller algorithm.

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