TORNERO SÁNCHEZ , José María

The following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that is, an algebroid embedded surface admitting an equation whose roots are Puiseux power series), using a set of exponents appearing in a root of an equation. The aim is knowing to which extent the well–known results for the...

La memoria se articula en tres capítulos. En el primer capítulo se fijan definiciones y propiedades conocidas. Superficies algebroides, explosiones, divisor excepcional, cono tangente. Así mismo se prueban resultados técnicos de interés. En el segundo capítulo se prueba fundamentalmente un Teorema de Resolución de Superficies en la línea del...

This paper extends previous results of the authors, concerning the behaviour of the equimultiple locus of algebroid surfaces under blowing–up, to arbitrary characteristic.

Hironaka's concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of the last decades in singularity theory. In fact, since then combinatorics have become a major tool in many important results. However, this seminal concept is still not enough to cope with some effective problems: for...

The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution process, both classical and modern.In this paper we explore how it changes by blowing–up.

The purpose of this paper is to give a down-to-earth proof of the well–known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.

We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.