Singularities and duality in the flat geometry of submanifolds of Euclidean spaces.
Singularities of convex hulls as fronts of Legendre varieties
We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphism. It turns out that the boundary of the convex hull is the front of a Legendre variety. Its singularities are classified up to contact diffeomorphism.