Free Resolutions of Fat Point Ideals on $P^2$
Abstract
By defining a fat point subscheme of to be a 0-dimensional subscheme defined by a sheaf of integrally closed ideals one extends the notion of fat point subschemes to allow infinitely near points. With this notion of fat points, this preprint determines the number of generators in each degree in a minimal homogeneous set of generators for the homogeneous ideal defining any fat point subscheme supported at points of any plane conic, smooth or not. Special cases for points on a cubic are also studied. All work is over an algebraically closed field of arbitrary characteristic.
Cite
@article{arxiv.alg-geom/9509002,
title = {Free Resolutions of Fat Point Ideals on $P^2$},
author = {Brian Harbourne},
journal= {arXiv preprint arXiv:alg-geom/9509002},
year = {2009}
}
Comments
plain tex, 15 pp. The preprint itself is not contained in the Duke archive; plainTeX textfile and dvi versions of this preprint can instead be obtained via the author's www site, http://www.math.unl.edu/~bharbour/ . Comments and requests can be directed to [email protected]