Functional moduli of singularities of convex hulls of manifolds of codimensions 1 and 2

In this paper we study singularities of convex hulls of smooth submanifolds of an affine space whose codimension is not greater than two. We prove that in spaces of dimension five or higher some of these singularities have functional moduli with respect to the group of diffeomorphisms of the ambient space that cannot be removed by small deformations of the manifold.
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