Classification of singularities at infinity of polynomials of degree 4 in two variables

Abstract

During the last years there is an increasing interest in the behaviour of polynomials at innity. In studying the family of levels curves f(x; y) = t one wants to know e.g the topological type of generic bres, the set of bifurcation values, the change of topology of the bre near bifurcation values, the monodromy at innity, the intersection form on bres. For classes of polynomials (e.g. tame polynomials) the changes in the topology depend only on the ane singular points and their singularity types. But in general also other eects (due to the non propernesss of the polynomial function) can change the bres. One calls this `singular behaviour at innity'.