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Fouli, Louiza; Mantero, Paolo; Xie, Yu

doi:10.1016/j.jalgebra.2017.11.002

Cited by 20 publications

(15 citation statements)

References 20 publications

(35 reference statements)

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“…Chudnovsky [4] showed that this is true if n = 2. Furthermore, the conjecture is known if Z is a set of general points by Fouli, Mantero, and Xie [15] (see also [10] if |Z| ≥ 2 n ).…”

Section: Conjectures By Chudnovsky and Demaillymentioning

confidence: 99%

Interpolation and the weak Lefschetz property

Nagel

Trok

2019

Trans. Amer. Math. Soc.

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Our starting point is a basic problem in Hermite interpolation theory, namely determining the least degree of a homogeneous polynomial that vanishes to some specified order at every point of a given finite set. We solve this problem if the number of points is small compared to the dimension of their linear span. This also allows us to establish results on the Hilbert function of ideals generated by powers of linear forms. The Verlinde formula determines such a Hilbert function in a specific instance. We complement this result and also determine the Castelnuovo-Mumford regularity of the corresponding ideals. As applications we establish new instances of conjectures by Chudnovsky and by Demailly on the Waldschmidt constant. Moreover, we show that conjectures on the failure of the weak Lefschetz property by Harbourne, Schenck, and Seceleanu as well as by Migliore, Miró-Roig, and the first author are true asymptotically. The latter also relies on a new result about Eulerian numbers.

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“…Chudnovsky [4] showed that this is true if n = 2. Furthermore, the conjecture is known if Z is a set of general points by Fouli, Mantero, and Xie [15] (see also [10] if |Z| ≥ 2 n ).…”

Section: Conjectures By Chudnovsky and Demaillymentioning

confidence: 99%

Interpolation and the weak Lefschetz property

Nagel

Trok

2019

Trans. Amer. Math. Soc.

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“…Demailly's conjecture is known for n = 2 over an algebraically closed field of characteristic 0 [5]. Demailly's conjecture for m = 1 (also called the Chudnovsky's conjecture) is known for very general points over an algebraically closed field of characteristic 0 [7], and for s ≥ 2 n very general points over an arbitrary algebraically closed field [4].…”

Section: Introductionmentioning

confidence: 99%

Demailly's conjecture on Waldschmidt constants for sufficiently many very general points in Pn

Chang

Jow

2020

Journal of Number Theory

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“…Also the authors of [7,4] proved the conjecture for any set of a binomial number of points in P N forming a star configuration, and the authors of [10] proved it for any set of at most 2 n points in very general position in P N . Recently, the authors of [12] achieve a remarkable result on Chudnovsky's conjecture. They show that the conjecture holds for any finite set of very general points in P N k , where k is an algebraically closed field of characteristic 0, which improves the result of [10].…”

Section: Introductionmentioning

confidence: 99%

“…[11,23]. Also see [12,10] for related works. Now consider a family S of a given points p 1 , · · · , p r (not necessarily generic).…”

Section: Introductionmentioning

confidence: 99%

Lower semi-continuity of the Waldschmidt constants

Bae

2019

Communications in Algebra

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In this paper, we study the Waldschmidt constant of a generalized fat point subscheme Z = m1p1 + · · · + mrpr of P 2 , where p1, · · · , pr are essentially distinct points on P 2 , satisfying the proximity inequalities. Furthermore, we prove its lower semi-continuity for r ≤ 8. Using this property, we also calculate the Waldschmidt constants of the fat point subschemes Z = p1 + · · · + p5 giving weak del Pezzo surfaces of degree 4.

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Chudnovsky's conjecture for very general points in PkN

Cited by 20 publications

References 20 publications

Interpolation and the weak Lefschetz property

Interpolation and the weak Lefschetz property

Demailly's conjecture on Waldschmidt constants for sufficiently many very general points in Pn

Lower semi-continuity of the Waldschmidt constants

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