Seminario Nacional de Geometría Algebraica en línea

Resumen:

In 2002 Artal, Cassou-Noguès, Luengo, and Melle Hernández, showed that the so-called topological zeta function of a germ of a complex hypersurface singularity is not a topological invariant. In doing so, they provided a closed formula for the local topological zeta function Z_{top} (F,s)_o of the suspension by N = 2 points of a germ of a hypersurface singularity f. In a Note added in proof to the previous work, Loeser suggests a general formula for the case of the suspension by N points. This generalization has apparently been unquestioned for more than two decades now, but it is easy to check that it is inaccurate. In this talk we correct the suggested formula and present a generalization for the motivic local zeta function. This is a joint work with Pedro González-Pérez and Manuel González-Villa.