We consider the last value $\hat {\mu}(\nu) $ of the vanishing sequence of $ H^ 0 (L) $ along
a divisorial or irrational valuation $\nu $ centered at $\mathcal {O} _ {\mathbb {P}^ 2, p} …

We consider rational surfaces Z defined by divisorial valuations ν ν of Hirzebruch surfaces.
We introduce concepts of non-positivity and negativity at infinity for these valuations and …

We prove that the Newton–Okounkov body associated to the flag E•:={X= Xr⊃ Er⊃{q}},
defined by the surface X and the exceptional divisor Er given by any divisorial valuation of …

This paper is devoted to determine the geometry of a class of smooth projective rational
surfaces whose minimal models are the Hirzebruch ones; concretely, they are obtained as …

We study the class of planar polynomial vector fields admitting Darboux first integrals of the
type∏ i= 1 rfi α i, where the α i's are positive real numbers and the fi's are polynomials …

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 …

In this paper, we provide new families of smooth projective rational surfaces whose Cox
rings are finitely generated. These surfaces are constructed by blowing-up points in …

We consider plane divisorial valuations of Hirzebruch surfaces and introduce the concepts
of non-positivity and negativity at infinity. We prove that the surfaces given by valuations of …

We introduce surfaces at infinity, a class of rational surfaces linked to curves with only one
place at infinity. The cone of curves of these surfaces is finite polyhedral and minimally …

We consider flags E•={X⊃ E⊃{q}}, where E is an exceptional divisor defining a non-positive
at infinity divisorial valuation νE of a Hirzebruch surface, qa point in E and X the surface …