ON THE SEIFERT FORM AT INFINITY ASSOCIATED WITH POLYNOMIAL MAPS

摘要

If a polynomeal map f:C~n → C has a nice behaviour at infinity (e.g.it is a "good polynomial"),then the Milnor fibration at infinity exists; in particular, one can define the Seifert form at infinity Γ (f) associated with f. In this paper we prove a Sebastiani-Thom type formula. Namely, if F:C~n→C and g: C~m → C are "good " polynomeals, and we define h=f direct+ g:C~n+m → C by h(x,y)=f(x) +g(y),then Γ (h)=(-1)~mnΓ(f) direct X Γ(g). This is the global analogue of the local result, proved independently by K.Sakamoto and P.Deligne for isolated hypersurface singularities.