On the valuative Nagata conjecture
C Galindo, F Monserrat, CJ Moreno-Ávila… - arXiv preprint arXiv …, 2022 - arxiv.org
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 …
projective surface to be minimal with respect to an ample divisor. These conditions involve a …
The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
C Galindo, F Monserrat, CJ Moreno-Ávila - arXiv preprint arXiv …, 2024 - arxiv.org
Let $ X $ be a rational surface obtained by blowing up at a configuration $\mathcal {C} $ of
infinitely near points over a Hirzebruch surface $\mathbb {F} _\delta $. We prove that there …
infinitely near points over a Hirzebruch surface $\mathbb {F} _\delta $. We prove that there …
[PDF][PDF] Global geometry of surfaces defined by non-positive and negative at infinity valuations
CJ Moreno Ávila - 2021 - core.ac.uk
We introduce the concepts of non-positive and negative at infinity plane valuation of a
Hirzebruch surface and determine nice global and local geometric properties of the surfaces …
Hirzebruch surface and determine nice global and local geometric properties of the surfaces …