2022
DOI: 10.1016/j.jpaa.2021.106811
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Extreme values of the resurgence for homogeneous ideals in polynomial rings

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Cited by 7 publications
(5 citation statements)
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“…We have learned that Harbourne, Kettinger, Zimmitti in [40] and DiPasquale, Drabkin in [19] proved independently that ρ a (I) < h if and only if ρ(I) < h. As pointed out in [19] Remark 2.3, the next result is similar as Proposition 4.1.3 of Denkert's thesis [18], as Lemma 4.12 in [20] and as Proposition 2.2 in [19].…”
Section: Asymptotic Resurgence and Stable Harbourne Conjecturesupporting
confidence: 60%
See 1 more Smart Citation
“…We have learned that Harbourne, Kettinger, Zimmitti in [40] and DiPasquale, Drabkin in [19] proved independently that ρ a (I) < h if and only if ρ(I) < h. As pointed out in [19] Remark 2.3, the next result is similar as Proposition 4.1.3 of Denkert's thesis [18], as Lemma 4.12 in [20] and as Proposition 2.2 in [19].…”
Section: Asymptotic Resurgence and Stable Harbourne Conjecturesupporting
confidence: 60%
“…It is clear from the definition that 1 ≤ ρ a (I) ≤ ρ(I). As pointed out in [40], DiPasquale, Francisco, Mermin, Schweig showed that ρ a (I) = sup{m/r : I (m) I r }, where I r is the integral closure of I r (see also [20] Corollary 4.14) .…”
Section: B Harbourne Conjectured In [4]mentioning
confidence: 92%
“…Remark 5.20. Corollary 5.19 can also be recovered by the recent Theorem 2.3 in [19] where the authors provide various examples and questions about computing the resurgence of homogeneous ideals.…”
mentioning
confidence: 88%
“…We also compute the Waldschmidt constant and the resurgence of the ideal defining a Hadamard fat grid (see Proposition 5.17 and Corollary 5. 19).…”
Section: Hadamard Fat Gridsmentioning
confidence: 99%
“…follows from [15] and [18] that the stable Harbourne conjecture is true when the resurgence or the asymptotic resurgence is strictly smaller than the bigheight h. A great source of examples for which the resurgence and asymptotic resurgence are known, comes either from the geometric side ( [4,5,10,24,25]) or from combinatorial side (see [30,28,19,29]).…”
Section: Introductionmentioning
confidence: 99%