Información del autor
Autor Melle Hernández, Alejandro |
Documentos disponibles escritos por este autor (54)
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Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | American Mathematical Society | 2008We offer an equivariant version of the classical monodromy zeta function of a singularity as a series with coefficients from the Grothendieck ring of finite G-sets tensored by the field of rational numbers. Main two ingredients of the definition[...]texto impreso
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Kluwer Academic Publishers | 2001A meromorphic germ at the origin in the complex space Cn is a ratio of two holomorphic germs on (Cn,0). After presentation of the basic definitions in the general context of arbitrary meromorphic germs the authors study the monodromy by calculat[...]texto impreso
Fernández de Bobadilla de Olarzábal, Javier José ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro ; Némethi, A. | Birkhauser Boston | 2007It is a very old and interesting open problem to characterize those collections of embedded topological types of local plane curve singularities which may appear as singularities of a projective plane curve C of degree d. The goal of the present[...]texto impreso
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Gusein Zade, S.M. ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Independent University of Moscow | 2016There are (at least) two different approaches to define an equivariant analogue of the Euler characteristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach eme[...]texto impreso
Gómez-Chacón, Inés María ; Baro González, Elías ; Barbero, Marta ; Capel Cuevas, Ángela ; Caravantes Tortajada, Jorge ; Contreras Tejada, Patricia ; Díaz-Cano Ocaña, Antonio ; Folgueira López, Marta ; Gómez Castro, David ; González Prieto, José Ángel ; González Ortega, Jorge ; Ivorra Benjamín, Pierre Paul ; Juan Llamas, María del Carmen ; Melle Hernández, Alejandro ; Pe Pereira, María ; Prieto Yerro, María Ángeles ; Sánchez Benito, María Mercedes ; Ramos del Olmo, Ángel Manuel | 2019-06-24Preparar al profesorado novel de matemáticas para una docencia universitaria de calidad, mediante el desarrollo de competencias y conocimiento estratégico para aprender a enseñar Matemáticas. Se desarrollan ejemplificaciones para ser implementadas.texto impreso
Gómez Chacón, Inés María ; Díaz-Cano Ocaña, Antonio ; Folgueira López, Marta ; Gómez Castro, David ; Ivorra, Benjamín Pierre Paul ; Martínez Aguinaga, Francisco Javier ; Ortuño, M. T. ; Ramos del Olmo, Ángel Manuel ; González Ortega, Jorge ; González Prieto, José Ángel ; Melle Hernández, Alejandro ; Sanchez Benito, Mercedes ; Barbero, Marta ; Pe Pereira, María ; Capel Cuevas, Ángela | UCM | 2020-06-29Preparar al profesorado novel de matemáticas para una docencia universitaria de calidad, en el desarrollo de competencias y conocimiento estratégico para aprender a enseñar Matemáticas. Ejemplificaciones e instrumentos de evaluación para el aula.texto impreso
We give a formula for the Euler characteristic of the Milnor fibre of any analytic function f of two variables. This formula depends on the intersection multiplicity, the multiplicity and the Milnor number of the branches of the germ of curve de[...]texto impreso
We give a formula for the Milnor number of a germ (X,0) subset of (C-n+1,0) defined by f=0, f=f(d)+f(d+k)+...epsilon C {x(0),...,x(n)}, and such that Sing(D) boolean AND Z (f(d+k)) = circle divide, where D=Z (f(d)) subset of P-C(n). We prove tha[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Editorial Complutense | 2000The article under review contains a study of the topology of a pair (P2,C), where C is an algebraic curve in the complex projective plane. The basic problem is to find invariants which are sensitive enough to distinguish many pairs, and for whic[...]texto impreso
The notion of the orbifold Euler characteristic came from physics at the end of the 1980s. Coincidence (up to sign) of the orbifold Euler characteristics is a necessary condition for crepant resolutions of orbifolds to be mirror symmetric. There[...]texto impreso
Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Springer | 2009The purpose of this paper is to describe the generating series of classes of Hilbert schemes of points on complex orbifolds. The computation takes place in the Grothendieck ring of complex quasi-projective varieties and uses the notion of ‘power[...]texto impreso
Artal Bartolo, Enrique ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | http://www.worldscientific.com | 2015-11In this work we deal with dicritical divisors, curvettes and polynomials.These objects have been one of the main research interests of S.S. Abhyanka during his last years. In this work we provide some elementary proofs of some S.S.Abhyankar and [...]texto impreso
For a complex quasi-projective manifold with a finite group action, we define higher order generalized Euler characteristics with values in the Grothendieck ring of complex quasi-projective varieties extended by the rational powers of the class [...]texto impreso
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Cambridge University Press | 2015-12We generalize the notions of the orbifold Euler characteristic and of the higher-order orbifold Euler characteristics to spaces with actions of a compact Lie group using integration with respect to the Euler characteristic instead of the summati[...]texto impreso
Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Springer | 2006Notions 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 [...]texto impreso
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Given a curve C on a projective nonsingular rational surface S, over an algebraically closed eld of characteristic zero, we are interested in the set C of linear systems L on S satisfying C 2 L, dimL 1, and the general member of L is a rationa[...]texto impreso
Luengo Velasco, Ignacio ; Melle Hernández, Alejandro ; Némethi, A. | American Mathematical Society | 2005Using superisolated singularities we present examples and counterexamples to some of the most important conjectures regarding invariants of normal surface singularities. More precisely, we show that the ``Seiberg-Witten invariant conjecture''(of[...]texto impreso
In this paper we show that the Euler characteristic of the generic fibre of a complex polynomial function f : C-n --> C can be easily computed using the Newton number of f. We apply this result to study polynomials with a finite number of criti[...]texto impreso
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An additive formula for the Milnor number of an isolated complex hypersurface singularity is shown. We apply this formula for studying surface singularities. Durfee's conjecture is proved for any absolutely isolated surface and a generalization [...]texto impreso
Melle Hernández, Alejandro ; Artal Bartolo, Enrique ; Cassou-Noguès, Pierrette ; Luengo Velasco, Ignacio | Société Mathématique de France | 2002-07In 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 f[...]texto impreso
We study the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a germ of a holomorphic function in two variables. It was known that there is at most one double pole for (any of) these zeta func[...]texto impreso
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Springer | 1999A meromorphic function on a compact complex analytic manifold defines a C? locally trivial bundle over the complement to a finite subset of the projective line CP1, the bifurcation set. The monodromy transformations of this bundle correspond to [...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Melle Hernández, Alejandro | Cambridge University Press | 2010This note provides a negative answer to the following question of A. H. Durfee [Invent. Math. 28 (1975), 231–241; ]: Is it true for arbitrary polynomials F(x,y,z) having an isolated singularity at the origin that the local monodromy is of finite[...]texto impreso
In this work we show a singular K3 surface S of such that producing a counter-example to a conjecture of Veys.texto impreso
Luengo Velasco, Ignacio ; Gusein-Zade, Sabir Medgidovich ; Melle Hernández, Alejandro | Independent University of Moscow | 2010-09We discuss different definitions of equivariant (with respect to an action of a finite group on a manifold) Hilbert schemes of zero-dimensional subschemes and compute generating series of classes of equivariant Hilbert schemes for actions of cyc[...]texto impreso
The main objects of this study are the poles of several local zeta functions: the Igusa, topological, and motivic zeta function associated to a polynomial or (germ of) holomorphic function in n variables. We are interested in poles of maximal po[...]texto impreso
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Azerb. Math. Soc | 2011Two quasi-projective varieties are called piecewise isomorphic if they can be stratified into pairwise isomorphic strata. We show that the m-th symmetric power Sm(Cn) of the complex affine space Cn is piecewise isomorphic to Cmn and the m-th sym[...]texto impreso
The author proves a generalization of the Teissier theorem [B. Teissier, Invent. Math. 40, 267-292 (1977; Zbl 0446.32002)] about expressing the topological determinacy order by the polar invariants. In this generalization the main assumption is [...]texto impreso
Artal Bartolo, Enrique ; Cassou-Noguès, Pierrette ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | American Mathematical Society | 2011The concept of ?-quasi-ordinary power series, which is a generalization of quasi-ordinary power series, was first introduced by H. Hironaka. In the paper under review, the authors study ?-quasi-ordinary power series and give a factorization theo[...]texto impreso
Fernández de Bobadilla de Olarzábal, Javier José ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro ; Némethi, A. | World Scientific Publishing Co. | 2007Let C be an irreducible projective plane curve in the complex projective space P(2). The classification of such curves, up to the action of the automorphism group PGL(3, C) on P(2), is a very difficult open problem with many interesting connecti[...]texto impreso
Melle Hernández, Alejandro ; Fernández de Bobadilla de Olarzábal, Javier José ; Luengo Velasco, Ignacio ; Némethi , A. | Oxford University Press (OUP) | 2006-01In 2002, L. Nicolaescu and the fourth author formulated a very general conjecture which relates the geometric genus of a Gorenstein surface singularity with rational homology sphere link with the Seiberg--Witten invariant (or one of its candidat[...]texto impreso
Artal Bartolo, Enrique ; Cassou-Noguès, Pierrette ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | American Mathematical Society | 2008In this article we show that for a given, reduced or non reduced, germ of a complex plane curve, there exists a local system of coordinates such that its log-canonical threshold at the singularity can be explicitly computed from the intersection[...]texto impreso
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Springer | 2007-09We discuss the notion of a power structure over a ring and the geometric description of the power structure over the Grothendieck ring of complex quasi-projective varieties and show some examples of applications to generating series of classes o[...]texto impreso
On the pre-lambda-ring structure on the Grothendieck ring of stacks and the power structures over it
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Cambridge Univ. Press | 2013-06We describe a pre-lambda-structure on the Grothendieck ring of stacks (originally studied by Torsten Ekedahl) and the corresponding power structures over it, discuss some of their properties and give some explicit formulae for the Kapranov zeta-[...]texto impreso
Artal Bartolo, Enrique ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Taylor & Francis | 2000In 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 n[...]texto impreso
Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Firat University | 1999In a previous paper the authors elaborated notions and technique which could be applied to compute such invariants of polynomials as Euler characteristics of fibres and zeta-functions of monodromy transformations associated with a polynomial. So[...]texto impreso
Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Nauka. S.-Peterburg. Otdel | 1999Let f = P/Q be a meromorphic function germ on (Cn+1, 0), where P,Q: (Cn+1, 0) ! (C, 0) are holomorphic germs. The authors [Funktsional. Anal. i Prilozhen. 32 (1998), no. 2, 26–35, 95; MR1647824 (99j:32040)] introduced a notion of Milnor fibers a[...]texto impreso
Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Elsevier Sci. | 2000-04We use the notion of Milnor fibres of the germ of a meromorphic function and the method of partial resolutions for a study of topology of a polynomial map at infinity (mainly for calculation of the zeta-function of a monodromy). It gives effecti[...]texto impreso
Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Birkhäuser Verlag | 1997We give a generalization of N. A'Campo's formula for the zeta-function of the monodromy of a singularity and show some examples of its applications.texto impreso
Although the theory of singularities of curves - resolution, classification, numerical invariants - goes through with comparatively little change in finite characteristic, pencils of curves are more difficult. Bertini's theorem only holds in a m[...]texto impreso
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | International Press | 2004Let R be either the Grothendieck semiring (semigroup with multiplication) of complex quasi-projective varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class \L of the complex affine line. We defin[...]texto impreso
Melle Hernández, Alejandro ; Artal Bartolo, Enrique ; Cassou-Noguès, Pierrette ; Luengo Velasco, Ignacio | American Mathematical Society | 2005-11The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motiv[...]texto impreso
Artal Bartolo, Enrique ; Cassou-Noguès, Pierrette ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Independent University of Moscow | 2013In this paper we study some properties of the class of nu-quasi-ordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize quasi-ordinar[...]texto impreso
Since the implementation of the Montreal Protocol and the Clean Air Act Amendment of 1990, the polyurethane industry has been searching for ways to reduce or eliminate auxiliary blowing agents (ABAs) from foam manufacturing processes. Many possi[...]texto impreso
Artal Bartolo, Enrique ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Cambridge University Press | 2006In this survey, we review part of the theory of superisolated surface singularities (SIS) and its applications including some new and recent developments. The class of SIS singularities is, in some sense, the simplest class of germs of normal su[...]texto impreso
Artal Bartolo, Enrique ; Cassou-Noguès, Pierrette ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Oxford University Press | 2002-02An 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 foll[...]texto impreso
En esta memoria se obtienen formulas que relacionan el numero de milnor de un germen de hipersuperficie compleja con singularidad aislada con la geometria de las hipersuperficies proyectivas definidas por los ceros de los polinomios homogéneos q[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio ; Escario Gil, Mario ; Fernández de Bobadilla de Olarzábal, Javier José ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Editorial Complutense | 2004We study properties of arrangements of rational plane curves. The existence of such curves with prescribed topological data has a lot of geometric restrictions. We show how to use the theory of singular complex analytic spaces to obtain such res[...]texto impreso
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Bartolo, E. A. ; Cassou-Nogués, P. ; Luengo, I. ; Melle Hernández, Alejandro | European Mathematical Society | 2017In 1982, Tamaki Yano proposed a conjecture predicting the b-exponents of an irreducible plane curve singularity germ that is generic in its equisingularity class. In this article, we prove the conjecture for the case in which the irreducible ger[...]texto impreso
Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Springer Verlag | 1998-04Let f be a meromorphic function germ on (Cn+1, 0); that is, f = P/Q, where P,Q: (Cn+1, 0)! (C, 0) are holomorphic germs. The authors introduce a notion of Milnor fibers and monodromy operators of the germ f around zero and infinity. Based on the[...]