Singularity exchange at the frontier of the space
  In deformations of polynomial functions one may encounter   ``singularity exchange at infinity'' when singular points disappear from the space and produce   ``virtual'' singularities which have an influence on the topology of the limit polynomial. We find several rules of this exchange phenomenon, in which the total quantity of singularity turns out to be not conserved in general. 
Dirk Siersma and Mihai Tibar