Kato-Matsumoto-type results for disentanglements

Abstract

We consider the possible disentanglements of holomorphic map germs $f \colon (\mathbb C^n,0) \to (\mathbb C^N,0)$, $n < N$, with nonisolated locus of instability $\operatorname{Inst}(f)$. The aim is to achieve lower bounds for their (homological) connectivity in terms of $\dim \operatorname{Inst}(f)$. Our methods apply in the case of corank $1$.