arXiv subjects

Alejandro Melle-Hernandez

Publications and source records attributed to Alejandro Melle-Hernandez.

2 recordsLinked to original sources

arXiv2004

Integration over spaces of non-parametrized arcs and motivic versions of the monodromy zeta function

We elaborate notions of integration over the space of arcs factorized by the natural $C^*$-action and over the space of non-parametrized arcs (branches). There are offered two motivic versions of the zeta function of the classical monodromy transformation of a germ of an analytic function on a smooth space. We indicate a direct formula which connects the naive motivic zeta function of J. Denef and F. Loeser with the classical monodromy zeta function.

math.AG↗

arXiv2004

Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points

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 schemes of zero-dimensional subschemes on a smooth quasi-projective variety as an exponent of that for the complex affine space of the same dimension. Specializations of this relation give formulae for generating series of such invariants of the Hilbert schemes of points as the Euler characteristic and the Hodge-Deligne polynomial.

math.AG↗