2014
DOI: 10.1016/j.jpaa.2013.04.012
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Containment results for ideals of various configurations of points in

Abstract: Guided by evidence coming from a few key examples and attempting to unify previous work of Chudnovsky, Esnault-Viehweg, Eisenbud-Mazur, Ein-Lazarsfeld-Smith, Hochster-Huneke and Bocci-Harbourne, Harbourne and Huneke recently formulated a series of conjectures that relate symbolic and regular powers of ideals of fat points in P N . In this paper we propose another conjecture along the same lines (Conjecture 3.9), and we verify it and the conjectures of Harbourne and Huneke for a variety of configurations of poi… Show more

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Cited by 47 publications
(70 citation statements)
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“…In algebraic geometry and in commutative algebra there has been recently a lot of interest in comparing usual (algebraic) and symbolic powers of homogeneous ideals, see for example [2], [10], [3]. If I ⊂ K[x 0 , x 1 , .…”
Section: The Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…In algebraic geometry and in commutative algebra there has been recently a lot of interest in comparing usual (algebraic) and symbolic powers of homogeneous ideals, see for example [2], [10], [3]. If I ⊂ K[x 0 , x 1 , .…”
Section: The Main Resultsmentioning
confidence: 99%
“…If the number of triple points is high when related to the number of lines, then F will be the only element of degree s in I (3) . On the other hand, the generators of I should be of relatively high degree.…”
Section: Proof Of the Main Resultsmentioning
confidence: 99%
“…More precisely, it is proven therein that removing any single point from among the 13 points of the finite projective plane P 2 F 3 together with all the lines passing through the removed point yields on the remaining 12 points the same incidence structure exhibited by the dual Hesse configuration of [8]. It is worth noting, however, that although they share the same combinatorial data and the property that I (3) I 2 , the dual Hesse configuration of [8] and the characteristic 3 counterexample of [2] behave very differently when viewed from the perspective of algebraic-geometric invariants associated to them (see [7] for a detailed account of the differences and computations of the resurgence for these counterexamples).…”
Section: Comparing Symbolic and Ordinary Powers Of Idealsmentioning
confidence: 92%
“…The entire incidence structure of the 12 points and 9 lines is projectively dual to the classical Hesse configuration given by the 9 flexes of a general plane cubic together with the 12 lines passing through pairs of these flexes. A characteristic 3 analogue of the counterexample of [8] was later given in [2]. More precisely, it is proven therein that removing any single point from among the 13 points of the finite projective plane P 2 F 3 together with all the lines passing through the removed point yields on the remaining 12 points the same incidence structure exhibited by the dual Hesse configuration of [8].…”
Section: Comparing Symbolic and Ordinary Powers Of Idealsmentioning
confidence: 95%
“…[2], [3], [10]. The first counterexample to the I (3) ⊂ I 2 containment for an ideal of points in P 2 announced in [6] has prompted another series of papers [1], [11], [13]. In all these works the authors study containment relations of the type I (m) ⊂ I r for a fixed homogeneous ideal I.…”
Section: Introductionmentioning
confidence: 99%