arXiv subjects

J. M. Tornero

Publications and source records attributed to J. M. Tornero.

4 recordsLinked to original sources

arXiv2006

Hironaka's characteristic polygon and effective resolution of surfaces

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 instance, giving a bound on the maximum number of blowing--ups to be performed on a surface before its multiplicity decreases. This short note shows why such a bounding is not possible, at least with the original definitions.

math.AG↗

arXiv2006

On simultaneous arithmetic progressions on elliptic curves

In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally point out open questions which focus on the most interesting aspects of the problem for us.

math.NT↗

arXiv2002

On Kummer extensions of the power series field

In this paper we study the Kummer extensions of the power series field $K=k((X_1,...,X_n)$, where $k$ is an algebraically closed field of arbitrary characteristic.

math.AC↗

arXiv2000

Computing the rational torsion of an elliptic curve using Tate normal form

It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n ($4 \leq n \leq 10$, or n = 12) lie in a one-parameter family. However, this fact does not appear to have been used ever for computing the torsion of an elliptic curve. We present here a extremely down-to-earth algorithm using the existence of such a family.

math.AG↗