2004
DOI: 10.1016/j.jpaa.2003.07.006
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The regularity of points in multi-projective spaces

Abstract: Let I =˝m 1 1 ∩ · · · ∩˝m s s be the deÿning ideal of a scheme of fat points in P n 1 × · · · × P n k with support in generic position. When all the mi's are 1, we explicitly calculate the CastelnuovoMumford regularity of I . In general, if at least one mi ¿ 2, we give an upper bound for the regularity of I , which extends a result of Catalisano, Trung and Valla.In this paper, we study the Castelnuovo-Mumford regularity of deÿning ideals of sets of points (reduced and non-reduced) in a multi-projective space P… Show more

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Cited by 17 publications
(8 citation statements)
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“…The benefit of studying this class of ideals is that we already have some information on the regularity of these ideals (see [9,11,14] for more on this).…”
Section: Points In Multi-projective Spacesmentioning
confidence: 99%
See 1 more Smart Citation
“…The benefit of studying this class of ideals is that we already have some information on the regularity of these ideals (see [9,11,14] for more on this).…”
Section: Points In Multi-projective Spacesmentioning
confidence: 99%
“…For our first set of examples, we consider the ideals of sets of points in P n1 × • • • × P nr . The benefit of studying this class of ideals is that we already have some information on the regularity of these ideals (see [9,11,14] for more on this).…”
Section: 1mentioning
confidence: 99%
“…In this situation there are several classifications. Giuffrida, Maggioni, and Ragusa [7], who helped to initiate the study of points in multiprojective spaces (see, for example [8,9,12,13,14,18,20,21,22] for more on these points), provided the first classification. They showed that ACM sets of points in P 1 × P 1 can be classified via their Hilbert functions.…”
Section: Introductionmentioning
confidence: 99%
“…[Hà07,SVTW06], try to unify these approaches and to generalize them [BC17]. When restricted to zero-dimensional closed subschemes of toric varieties, [HVT04,SVTW06] studies alternative definitions for fat points in multiprojective space and [S ¸S16] studies the regularity (in the sense of [MS03]) of homogeneous ideals generated by regular sequences over simplicial toric varieties.…”
Section: Regularity For Zero-dimensional Closed Subschemesmentioning
confidence: 99%