We consider surfaces X defined by plane divisorial valuations ν of the quotient field of the
local ring R at a closed point p of the projective plane P 2 over an arbitrary algebraically …

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 …

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 …

The aim of this paper is to provide an explicit basis of the miniversal deformation of a
monomial curve defined by a free semigroup--these curves make up a notable family of …

We construct evaluation codes given by weight functions defined over polynomial rings in
m≥ 2 indeterminates. These weight functions are determined by sets of m− 1 weight …

We give an algorithm for deciding whether a planar polynomial differential system has a first
integral which factorizes as a product of defining polynomials of curves with only one place …

Plane valuations at infinity are classified in five types. Valuations in one of them determine
weight functions which take values on semigroups of\mathbb Z^ 2 Z 2. These semigroups …

Let C be a curve with only one place at infinity, and let SC,∞ be its semigroup at infinity. It is
known that this semigroup is generated by a δ-sequence in N> 0. In this work we study the …

Evaluation codes are a particular construction of error-correcting codes, consisting of
evaluating functions at rational places of certain geometric objects. Classical examples are …