2000
DOI: 10.1016/s0022-4049(99)00100-0
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Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions

Abstract: In this paper we study some problems concerning bigraded ideals. By introducing the concept of bigeneric initial ideal, we answer an open question about diagonal subalgebras and we give a necessary condition for a function to be the bigraded Hilbert function of a bigraded algebra. Moreover, we give an upper bound for the regularity of a bistable ideal in terms of the degrees of its generators

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Cited by 33 publications
(91 citation statements)
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“…In particular, we show how to use reg-num v (M) to determine bounds on the multigraded regularity of M as defined in [11]. As well, we relate reg-num v (M) to the resolution regularity vector of M as defined by [1,14].…”
Section: Connections With Other Notions Of Regularitymentioning
confidence: 99%
“…In particular, we show how to use reg-num v (M) to determine bounds on the multigraded regularity of M as defined in [11]. As well, we relate reg-num v (M) to the resolution regularity vector of M as defined by [1,14].…”
Section: Connections With Other Notions Of Regularitymentioning
confidence: 99%
“…As L is generic, the initial ideal in(I) is the multigraded generic initial ideal of I with respect to >. Hence in(I) is Borel fixed is the multigraded sense, see [1]. In characteristic 0 this means that if a monomial M is in in(I) and t ij |M then t ik M/t ij is in in(I) as well for all the k > j.…”
Section: The Generic Casementioning
confidence: 99%
“…See e.g., [13]. Also, for r = 2, G-generic initial ideals and strongly color-stable ideals are considered in [2]. Now we define colored algebraic shifting.…”
Section: Colored Algebraic Shiftingmentioning
confidence: 99%
“…Let be a set of indices, X = {x τ : τ ∈ } a set of variables and K[X] the polynomial ring over a field K in the set of variables X. Consider the set of variablesX = {x τ, [k] : [1] x τ j , [2] · · · x τ j , There is a nice relationship between polarization and graded Betti numbers. For a finitely generated graded ideal I ⊂ K[X], we define the graded Betti numbers of I by The following nice fact is known: Let I be a monomial ideal of K[x 1,1 , .…”
Section: Polarization and Squarefree Stable Operatorsmentioning
confidence: 99%
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