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Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points
Sabir M. Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernandez
The power structure over the Grothendieck (semi)ring of complex quasi-projective varieties constructed by the authors is used to express the generating series of classes of Hilbert…
Integration over spaces of non-parametrized arcs and motivic versions of the monodromy zeta function
Sabir M. Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernandez
We elaborate notions of integration over the space of arcs factorized by the natural -action and over the space of non-parametrized arcs (branches). There are offered two moti…
An exponential function on the set of varieties
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernandez
Let be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck rin…
On the zeta-function of a polynomial at infinity
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernandez
We 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 c…