Generic sections of essentially isolated determinantal singularities
Résumé
We study the essentially isolated determinantal singularities (EIDS), defined by Ebeling and Gusein-Zade [S. M. Gusein-Zade and W. Ebeling, On the indices of 1-forms on determinantal singularities, Tr. Mat. Inst. Steklova 267 (2009) 119-131], as a generalization of isolated singularity. We prove in dimension 3, a minimality theorem for the Milnor number of a generic hyperplane section of an EIDS, generalizing the previous results by Snoussi in dimension 2. We define strongly generic hyperplane sections of an EIDS and show that they are still EIDS. Using strongly general hyperplanes, we extend a result of Le concerning the constancy of the Milnor number.