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arXiv · 2208.11041

On the valuative Nagata conjecture

Carlos Galindo·Francisco Monserrat·Carlos-Jesús Moreno-Ávila·Julio José Moyano-Fernández
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Abstract

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.

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Carlos Galindo, Francisco Monserrat, Carlos-Jesús Moreno-Ávila, Julio José Moyano-Fernández. 2022-08-23. On the valuative Nagata conjecture. https://doi.org/10.1007/s40687-025-00500-2

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