On the valuative Nagata conjecture

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.

Comments are welcome

References in corpus (4)

• Discrete behavior of Seshadri constants on surfaces
• On Seshadri constants and point-curve configurations
• On the degree of curves with prescribed multiplicities and bounded negativity
• Newton-Okounkov bodies and Picard numbers on surfaces

Cited by in corpus (1)

• The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces