A’Campo type equations and integrals with respect to the Euler characteristic

Abstract

The integral with respect to the Euler characteristic was first defined by O. Viro in 1988. Just after that it was understood that a number of equations obtained earlier already included implicitly this integral written in other terms. Thus one can say that, as the creator of the notion of the integral with respect to the Euler characteristic, Viro had some predecessors. One of them was Norbert A'Campo with his equations for the Euler characteristic of the Milnor fibre of a germ of a holomorphic function and for its monodromy zeta function it terms of a resolution. Moreover, it seems that he was the only one who (at that moment) wrote down a multiplicative analogue of this integral. This sort of expressions are often called A'Campo type equations.