TY - JOUR

T1 - Resolutions of subsets of finite sets of points in projective space

AU - Diaz, Steven P.

AU - Geramita, Anthony V.

AU - Migliore, Juan C.

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2000

Y1 - 2000

N2 - 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, 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.

AB - 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, 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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U2 - 10.1080/00927870008827184

DO - 10.1080/00927870008827184

M3 - Article

AN - SCOPUS:0034550036

VL - 28

SP - 5715

EP - 5733

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 12

ER -