On weighted bounded negativity for rational surfaces

C Galindo, F Monserrat, CJ Moreno-Ávila - arXiv preprint arXiv …, 2024 - arxiv.org
The weighted bounded negativity conjecture considers a smooth projective surface $ X $
and looks for a common lower bound on the quotients $ C^ 2/(D\cdot C)^ 2$, where $ C …

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 …