Free Resolutions of Fat Point Ideals on $P^2$

Brian Harbourne

doi:10.1016/s0022-4049(96)00126-0

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arXiv · alg-geom/9509002

Free Resolutions of Fat Point Ideals on $P^2$

Brian Harbourne

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Abstract

By defining a fat point subscheme of $P^2$ 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.

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Brian Harbourne. 1998-06-18. Free Resolutions of Fat Point Ideals on $P^2$. https://doi.org/10.1016/s0022-4049(96)00126-0

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