Resolutions of subsets of finite sets of points in projective space
作者:
Steven P. Diaz,
Anthony V. Geramita,
Juan C. Migliore,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 12
页码: 5715-5733
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008827184
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
Given a finite setX, 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"insideX. 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, via two very different kinds of counterexamples, that this generic resolution is not always achieved. 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.
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