Kato-Matsumoto-type results for disentanglements

Abstract

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

21 pages, 4 figures. Final version after acceptance for publication