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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
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
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
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
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
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
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[...]
