Symbolic powers of generalized star configurations of hypersurfaces

Lin, Kuei-Nuan; Shen, Yi-Huang

doi:10.48550/arxiv.2106.02955

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2021

2022

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Cited by 2 publications

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“…The formula has been quite well received and seen many applications since its discovery (cf. [2,4,5,13,14,16,18,19,20,22]).…”

Section: Introductionmentioning

confidence: 99%

Integral closures of powers of sums of ideals

Banerjee¹,

Harbourne²

2022

Preprint

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Let be a field, let A and B be polynomial rings over , and let S = A ⊗ B. Let I ⊆ A and J ⊆ B be monomial ideals. We establish a binomial expansion for rational powers of I + J ⊆ S in terms of those of I and J. Particularly, for u ∈ Q + , we prove thatand that the sum on the right hand side is a finite sum. We further give a sufficient condition for this formula to hold for the integral closures of powers of I + J in terms of those of I and J. Under this sufficient condition, we also provide precise formulas for the depth and regularity of (I + J) k in terms of those of powers of I and J. Our methods are linear algebra in nature, making use of the characterization of rational powers of a monomial ideal via optimal solutions to linear programming problems.

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“…The formula has been quite well received and seen many applications since its discovery (cf. [2,4,5,13,14,16,18,19,20,22]).…”

Section: Introductionmentioning

confidence: 99%

Integral closures of powers of sums of ideals

Banerjee¹,

Harbourne²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…From a commutative algebra perspective, ideals defining star configurations represent an interesting class, since a great amount of information is known about their free resolutions, Hilbert functions and symbolic powers (see for instance [13,14,11,22,24,2,3,28,23]). In this article we study their Rees algebras, about which little is currently known (see for instance [18,12,26,5]).…”

Section: Introductionmentioning

confidence: 99%