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<p>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.</p>

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On the valuative Nagata conjecture

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月23日

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  • Carlos Galindo,
  • Francisco Monserrat,
  • Carlos-Jesús Moreno-Ávila,
  • Julio-Jose Moyano-Fernández

摘要

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.