#### Title

Resolutions of Subsets of Finite Sets of Points in Projective Space

#### Document Type

Article

#### Date

6-29-1999

#### Keywords

tbd

#### Disciplines

Mathematics

#### Description/Abstract

Given a finite set, X, of points in projective space for which the Hilbert function is known, a standard result says that there exists a subset of this finite set whose Hilbert function is "as big as possible" inside X. Given a finite set of points in projective space for which the minimal free resolution of its homogeneous ideal is known, what can be said about possible resolutions of ideals of subsets of this finite set? We first give a maximal rank type description of the most generic possible resolution of a subset. Then we show that this generic resolution is not always achieved, by incorporating an example of Eisenbud and Popescu. However, we show that it is achieved for sets of points in projective two space: given any finite set of points in projective two space for which the minimal free resolution is known, there must exist a subset having the predicted resolution.

#### Recommended Citation

Diaz, Steven P.; Geramita, Anthony V.; and Migliore, Juan C., "Resolutions of Subsets of Finite Sets of Points in Projective Space" (1999). *Mathematics - All Scholarship*. 138.

https://surface.syr.edu/mat/138

#### Source

Harvested from arXiv.org

## Additional Information

This is a manuscript is from arXiv.org, for more information see http://arxiv.org/abs/math/9906204