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Transcendental versions in C n of the Nagata conjecture

Abstract : The Nagata Conjecture is one of the most intriguing open problems in the area of curves in the plane. It is easily stated. Namely, it predicts that the smallest degree d of a plane curve passing through r ≥ 10 general points in the projective plane P 2 with multiplicities at least l at every point, satisfies the inequality d > √ r · l. This conjecture has been proven by M. Nagata in 1959, if r is a perfect square greater than 9. Up to now, it remains open for every non-square r ≥ 10, after more than a half century of attention by many researchers. In this paper, we formulate new transcendental versions of this conjecture coming from pluripotential theory and which are equivalent to a version in C n of the Nagata Conjecture.
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https://hal.archives-ouvertes.fr/hal-02160418
Contributor : Stephanie Nivoche <>
Submitted on : Wednesday, June 19, 2019 - 4:14:45 PM
Last modification on : Monday, October 12, 2020 - 2:28:06 PM

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  • HAL Id : hal-02160418, version 1
  • ARXIV : 1906.08518

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Stephanie Nivoche. Transcendental versions in C n of the Nagata conjecture. 2019. ⟨hal-02160418⟩

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