Saturation and vanishing ideals

Gimenez, Philippe; Ruano, Diego; Rodrigo, San-José,

doi:10.1007/s40863-022-00330-y

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2023

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“…Saturation of an ideal appears in [6] to compute the vanishing ideal of a finite set of rational points in projective space. Let F q be a finite field, I be an graded ideal of F q [x 1 , .…”

Section: Introductionmentioning

confidence: 99%

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The saturation number of c-bounded stable monomial ideals and their powers

2022

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Let S = K[x1, . . . , xn] be the polynomial ring over a field K and m = (x1, . . . , xn) be the irredundant maximal ideal of S. For an ideal I ⊂ S, let sat(I) be the minimum number k for which I : m k = I : m k+1 . In this paper, we compute the saturation number of irreducible monomial ideals and their powers. We apply this result to find the saturation number of the ordinary powers and symbolic powers of some families of monomial ideals in terms of the saturation number of irreducible components appearing in an irreducible decomposition of these ideals. Moreover, we give an explicit formula for the saturation number of monomial ideals in two variables.

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Section: Introductionmentioning

confidence: 99%

“…, x n ] such that (I(P n−1 Fq ) : I) = I(P n−1 Fq ) and X = V (I) ⊂ P n−1 Fq . In [6] the authors show that I(X) = (I + I(P n−1 Fq )) sat . Notice that I(P n−1 Fq ) = (x q i x j − x i x q j : 1 ≤ i < j ≤ n) (see [8]).…”

Section: Introductionmentioning

confidence: 99%