We give necessary and sufficient conditions for a divisor class on smooth projective
anticanonical rational surfaces to be the class of a smooth rational curve of self-intersection …

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 characterize the rational surfaces X which have a finite number of (—l)-curves under the
assumption that—Kxis nef (ie, the intersection number ofKx with any effective divisor on X is …

We prove that every projective rational surface of type (n, m) has only a finite number of (-1)
curves and only a finite number of (-2) curves, where n and m are nonnegative integers …

We prove the finite generation of the monoid of effective divisor classes on a Platonic
rational surface, then derive some consequences. We also show the vanishing of the …

Abstract top We study the geometry of a rational surface of Kodaira type IV by giving the
nature of its integral curves of self-intersection less than zero, in particular we show that they …

We give a numerical criterion for ensuring the finite generation of the effective monoid of the
surfaces obtained by a blowing-up of the projective plane at the supports of zero …

We characterize the rational surfaces X which have a finite number of (− 1)-curves under the
assumption that− KX is nef, where KX is a canonical divisor on X, and has self-intersection …

The aim of this paper is to give a geometric characterization of the finite generation of the
Cox rings of anticanonical rational surfaces. This characterization is encoded in the finite …

Using the high symmetry in the geometry of a smooth projective quadric, we construct
effectively new families of smooth projective rational surfaces whose nef divisors are regular …