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As already done for the matrix case for example in [Joe Harris, AlgebraicGeometry - A first course, p.256] we give a parametrization of the Bouligandtangent cone of the variety of tensors of bounded TT rank. We discuss how theproof generalizes to any binary hierarchical format. The parametrization can berewritten as an orthogonal sum of TT tensors. Its retraction onto the varietyis particularly easy to compose. We also give an implicit description of thetangent cone as the solution of a system of polynomial equations.

Tangent Cones to TT Varieties