On the Milnor fibration of certain Newton degenerate functions

Abstract

It is well known that the diffeomorphism-type of the Milnor fibration of a (Newton) non-degenerate polynomial function $f$ is uniquely determined by the Newton boundary of $f$. In the present paper, we generalize this result to certain degenerate functions, namely we show that the diffeomorphism-type of the Milnor fibration of a (possibly degenerate) polynomial function of the form $f=f^1\cdots f^{k_0}$ is uniquely determined by the Newton boundaries of $f^1,\ldots, f^{k_0}$ if $\{f^{k_1}=\cdots=f^{k_m}=0\}$ is a non-degenerate complete intersection variety for any $k_1,\ldots,k_m\in \{1,\ldots, k_0\}$.