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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[...]
