In this paper we generalise results of Craveiro de Carvalho () in two ways. First we prove the following fact.
PROPOSITION 1. Given any smooth submanifold M of real projective space ℙn, for L in an open dense subset of the space of codimension 2 subspaces of ℙnwe have
(a) L meets M transversally and
(b) the pencil of hyperplanes through L have at worst Morse (A1) contact with M.
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