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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[...]
