Singularity Exchange at Infinity

Abstract. In families of polynomial functions one may encounter “singularity exchange at infinity ” when singular points escape from the space and produce “virtual ” singularities of the limit polynomial, which have themselves an influence on the topology. The total quantity of singularity involved in this phenomenon may not be conserved. Inspite of the fact that some of the ingredients do not behave well in deformations, we prove semi-continuity results which enable us to find rules of the exchange phenomenon. 1