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Dive into the research topics where I. Luengo is active.

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Featured researches published by I. Luengo.


Annales Scientifiques De L Ecole Normale Superieure | 2002

Monodromy conjecture for some surface singularities

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

Normal forms and moduli spaces of curve singularities with semigroup (2p,2q,2pq+d)

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

THE DENEF–LOESER ZETA FUNCTION IS NOT A TOPOLOGICAL INVARIANT

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

On the Zeta-function of a polynomial at infinity

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

Bifurcations and topology of meromorphic germs

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

On the topology of a generic fibre of a polynomial function

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

Integration over spaces of nonparametrized arcs and motivic versions of the monodromy zeta function

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

On Some Conjectures About Free and Nearly Free Divisors

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

Codes on Drinfeld Modular Curves

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

Yano’s conjecture for two-Puiseux-pair irreducible plane curve singularities

Enrique Artal Bartolo; Pierrette Cassou-Noguès; I. Luengo; A. Melle-Hernández

In 1982, Yano proposed a conjecture predicting the

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A. Melle-Hernández

Complutense University of Madrid

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A. Melle Hernández

Complutense University of Madrid

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Gerhard Pfister

Kaiserslautern University of Technology

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A. Melle Hernandez

Spanish National Research Council

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