Información del autor
Autor Luengo Velasco, Ignacio |
Documentos disponibles escritos por este autor (61)
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We present a method to find curves over the finite field F-3 with many rational points. The method is based in an arithmetic study of linear systems of projective plane curves of a given degree and prescribed singularities. We have found curves [...]texto impreso
The topological theory of dicritical divisors is algebracized which makes it valid for nonzero characteristic as well as mixed characteristic.texto impreso
Let K be a field of characteristic O, and let R denote K[X] or K[[X]]. It is well known that the roots of a polynomial FisinR[Z] are fractional powers series in K[[X 1d/]], where Kmacr is a finite extension of K and disin N, and they can be obta[...]texto impreso
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
In this paper we present an example of a family of surface singularities which is Zariski-equisingular for a transversal projection, but it is not Zariski-equisingular for a generic projection.texto impreso
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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
It is a well-known result that one can associate to each embedded algrebroid surfaces (E.A.S.), such that mult(s)=2, and algebroid curve c(v) (not necesarilly reduced). On the other hand, is [5] we associate to each E.A.S. W a finite weighted tr[...]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
Rodríguez-Palánquex, María Cruz ; García Villalba, Luis Javier ; Luengo Velasco, Ignacio | Springer Verlag | 2001The aim of this paper is to present an exhaustive algebraic study of a new class of curves, the so-called Quasihermitian curves (that includes the Hermitian curves), computing its genus. These curves allow to construct good algebraic geometric G[...]texto impreso
Given a real analytic function f(x, y) with one critical point P-0, we Study deformations f(1) of f such that, for any t not equal 0, the analytic function f(t) has no critical points in a neighborhood of P-0. We give explicitly a deformation wi[...]texto impreso
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
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
Imaña Pascual, José Luis ; Luengo Velasco, Ignacio | Institute of Electrical and Electronics | 2020-05The rapid development of quantum computing constitutes a significant threat to modern Public-Key Cryptography (PKC). The use of Shor's algorithm with potential powerful quantum computers could easily break the two most widely used public key cry[...]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
We prove the existence of families of germs of holomorphic vector fields in Cm without a separatrix, in every complex dimension m bigger than or equal to 4.texto impreso
Oblatum 28-XII-1988 & 26-III-1990 & 10-X-1990 & 13-VI-1991 & 30-IX-1991. Supported by Université de Toulouse, CONACYT-CNRS and CAICYT-87-336 Fulltext Previewtexto 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
Quantum computers have the potential to solve difficult mathematical problems efficiently, therefore meaning an important threat to Public-Key Cryptography (PKC) if large-scale quantum computers are ever built. The goal of Post-Quantum Cryptogra[...]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
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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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
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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
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
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
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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
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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
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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
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[...]