Geom Dedicata (2017) 186:173–180 DOI 10.1007/s10711-016-0184-y ORIGINAL PAPER Minimal Whitney stratification and Euler obstruction of discriminants G. F. Barbosa 1 · N. G. Grulha Jr. 2 · M. J. Saia 2 Received: 9 April 2014 / Accepted: 21 July 2016 / Published online: 28 July 2016 © Springer Science+Business Media Dordrecht 2016 Abstract In this work we show how to obtain the minimal Whitney stratification of the discriminant of finitely determined map germs from (C m , 0) to (C p , 0), of corank one if n < p, and only with A k singularities, when m = n + p with n ≥ 0. We apply the theory developed by Gaffney which shows how to compute a Whitney stratification of discriminants of any finitely determined holomorphic map germ in the nice dimensions of Mather, or in its boundary. For the pairs cited above we show that both stratifications coincide. We also compute the local Euler obstruction at 0 in a class of discriminants of finitely determined map germs from C n+ p to C p with n ≥ 0 and only with A k singularities. Keywords Minimal Whitney stratification · Discriminant of map germs · Stable types of singularities Mathematics Subject Classification (2010) 58C27 · 58K65 · 32S15 · 32S30 · 58K15 The first author was partially supported by CNPq (grant 474289/2013-3). The second author was partially supported by CNPQ (grants 474289/2013-3 and 303641/2013-4) and by FAPESP (grants 2013/11258-9 and 2015/16746-7). The third author was partially supported by CNPq (grants 482183/2013-6 and 302814/2013-2) and by FAPESP (grant 2014/00304-2). B N. G. Grulha Jr. njunior@icmc.usp.br G. F. Barbosa grazielle@dm.ufscar.br M. J. Saia mjsaia@icmc.usp.br 1 Universidade Federal de São Carlos, Centro de Ciências Exatas e de Tecnologia, São Carlos, SP, Brazil 2 Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação-USP, São Carlos, SP, Brazil 123