On the valuative Nagata conjecture

We provide several equivalent conditions for a plane divisorial valuation of a smooth projective surface to be minimal with respect to an ample divisor. These conditions involve a valuative Seshadri constant and other global tools of the surface defined by the divisorial valuation. As a consequence,...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Galindo, Carlos, Monserrat, Francisco, Moreno-Ávila, Carlos-Jesús, Moyano-Fernández, Julio José
Format: Article
Language:English
Subjects:
Equivalence
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Summary:We provide several equivalent conditions for a plane divisorial valuation of a smooth projective surface to be minimal with respect to an ample divisor. These conditions involve a valuative Seshadri constant and other global tools of the surface defined by the divisorial valuation. As a consequence, we derive several equivalent statements for the valuative Nagata conjecture and some related results.
ISSN:2331-8422