On Intersections with Hypersurfaces and Normal Pseudo-flatness

摘要

We study the behaviour of the families of hypersurfaces that are applied in [4] to estimate the Lojasiewicz exponent and the exponent of separation at infinity. We prove that the hypersurfaces for which ν(Z·H)_S, c) is minimal are to be smooth along a subset of Z ∩ S and to meet some algebraic cones along the tangent space to S.