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 add a reasonable hypothesis in Theorem 1 in Rev. Mat. Iberoam. 31 (2015) no. 4, 1131–
1140, in order to make it correct. We adopt the terminology and notation in [1]. It seems that …

We mainly give a numerical condition to ensure the finite generation of the effective monoids
of some smooth projective rational surfaces. These surfaces are constructed from the blow …

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 …

We determine the fixed locus of the anticanonical complete linear system of a given
anticanonical rational surface. The case of a geometrically ruled rational surface is fully …

We define the notion of Platonic surfaces. These are anticanonical smooth projective
rational surfaces defined over any fixed algebraically closed field of arbitrary characteristic …

Effective construction of some Eckardt surfaces is given. In particular, not only their Picard
number may be big but also an anticanonical divisor may have a very large number of …

We prove the finite generation of the monoid of effective divisor classes on a smooth
projective rational surface X endowed with an anticanonical divisor such that all its …