I. Luengo
Complutense University of Madrid
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by I. Luengo.
Annales Scientifiques De L Ecole Normale Superieure | 2002
E. Artal Bartolo; Pierrette Cassou-Noguès; I. Luengo; A. Melle Hernández
In this work we give a formula for the local Denef–Loeser zeta function of a superisolated singularity of hypersurface in terms of the local Denef–Loeser zeta function of the singularities of its tangent cone. We prove the monodromy conjecture for some surfaces singularities. These results are applied to the study of rational arrangements of plane curves whose Euler–Poincare characteristic is three.
Archive | 1990
I. Luengo; Gerhard Pfister
This work has been possible thanks to a Scientific Agreement between the Universidad Complutense and the Humboldt Universitaet. This cooperation agreement supported our stay in the Bereich Algebra and Departamento de Algebra respectively.
Journal of The London Mathematical Society-second Series | 2002
E. Artal Bartolo; Pierrette Cassou-Noguès; I. Luengo; A. Melle Hernández
An example is given which shows that the Denef–Loeser zeta function (usually called the topological zeta function) associated to a germ of a complex hypersurface singularity is not a topological invariant of the singularity. The idea is the following. Consider two germs of plane curves singularities with the same integral Seifert form but with different topological type and which have different topological zeta functions. Make a double suspension of these singularities (consider them in a 4-dimensional complex space). A theorem of M. Kervaire and J. Levine states that the topological type of these new hypersurface singularities is characterized by their integral Seifert form. Moreover the Seifert form of a suspension is equal (up to sign) to the original Seifert form. Hence these new singularities have the same topological type. By means of a double suspension formula the Denef–Loeser zeta functions are computed for the two 3-dimensional singularities and it is verified that they are not equal.
Bulletin Des Sciences Mathematiques | 2000
S. M. Gusein-Zade; I. Luengo; A. Melle-Hernández
A polynomial function defines a locally trivial fibre bundle over the complement to a finite set in the target C. Objects connected with this fibration (say, monodromy operators and, in particular, the monodromy operator of the polynomial at infinity) are in some sense global. The idea of the paper is to localize computations of the zeta-functions of monodromy transformations for a polynomial, i.e., to express them in local terms. It is done with the use of the notion of Milnor fibres of the germ of a meromorphic function and the methods of calculation of the corresponding zeta-functions elaborated by the authors. It gives effective methods of computation of the zeta-function for a number of cases and a criterium for a value to be atypical at infinity.
Archive | 2001
S. M. Gusein-Zade; I. Luengo; Alejandro Melle Hernández
Maps defined by polynomial functions are traditional objects of interest in algebraic geometry and singularity theory. A polynomial P in n complex variables defines a map P : ℂ n → ℂ. The map P is not a locally trivial flbration over critical values of P. However, since the source ℂ n is not compact, the map P fails to be a locally trivial fibration over some other values as well. It is well known that a polynomial map defines a locally trivial fibration over the complement to a finite set in ℂ (the bifurcation set of P): [41, 45, 47].
Communications in Algebra | 2000
E. Artal; I. Luengo; A. Melle
In this work we study the topologies of the fibres of some families of complex polynomial functions with isolated critical points. We consider polynomials with some transversality conditions at infinity and compute explicitly its global Milnor number μ(f). the invariant λ(f) and therefore the Euler characteristic of its generic fibre. We show that under some mild ransversality condition (transversal at infinity) the behavior of f at infinity is good and the topology of the generic fibre is determined by the two homogeneous parts of higher degree of f Finally we study families of polynomials, called two-term polynomials. This polynomials may have atypical values at infinity. Given such a two-term polynomial f we characterize its atypical values by some invariants of f. These polynomials are a source of interesting examples.
arXiv: Algebraic Geometry | 2006
S. M. Gusein-Zade; I. Luengo; A. Melle-Hernández
Notions of integration of motivic type over the space of arcs factorized by the natural C*-action and over the space of nonparametrized arcs (branches) are developed. As an application, two motivic versions of the zeta function of the classical monodromy transformation of a germ of an analytic function on ℂd are given that correspond to these notions. Another key ingredient in the construction of these motivic versions of the zeta function is the use of the so-called power structure over the Grothendieck ring of varieties introduced by the authors.
arXiv: Algebraic Geometry | 2017
Enrique Artal Bartolo; Leire Gorrochategui; I. Luengo; A. Melle-Hernández
In this paper we provide infinite families of non-rational irreducible free divisors or nearly free divisors in the complex projective plane. Moreover, their corresponding local singularities can have an arbitrary number of branches. All these examples contradict some of the conjectures proposed by Dimca and Sticlaru. Our examples say nothing about the most remarkable conjecture by A. Dimca and G. Sticlaru, which predicts that every rational cuspidal plane curve is either free or nearly free.
Archive | 2000
Bartolomé López; I. Luengo
In this work, we improve the estimate given by Manin and Vladut (cf. [7]) of the complexity of constructing codes on Drinfeld modular curves (Proposition 15). This improvement is mainly a consequence of Propositions 8, 10 and 11.
Publications of The Research Institute for Mathematical Sciences | 2017
Enrique Artal Bartolo; Pierrette Cassou-Noguès; I. Luengo; A. Melle-Hernández
In 1982, Yano proposed a conjecture predicting the