On the valuative Nagata conjecture
arXiv:2208.11041 · doi:10.1007/s40687-025-00500-2
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.
arXiv commentComments are welcome
References in corpus (10)
- Seshadri constants on algebraic surfaces
- Local positivity of linear series on surfaces
- Vanishing sequences and Okounkov bodies
- Discrete behavior of Seshadri constants on surfaces
- Restrictions on Seshadri constants on surfaces
- Seshadri constants and special configurations of points in the projective plane
- On Seshadri constants and point-curve configurations
- Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces
- On the degree of curves with prescribed multiplicities and bounded negativity
- Newton-Okounkov bodies and Picard numbers on surfaces