Tensor ranks on tangent developable of Segre varieties

Edoardo Ballico 1 Alessandra Bernardi 2
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We describe the stratification by tensor rank of the points belonging to the tangent developable of any Segre variety. We give algorithms to compute the rank and a decomposition of a tensor belonging to the secant variety of lines of any Segre variety. We prove Comon's conjecture on the rank of symmetric tensors for those tensors belonging to tangential varieties to Veronese varieties.
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Edoardo Ballico, Alessandra Bernardi. Tensor ranks on tangent developable of Segre varieties. Linear and Multilinear Algebra, Taylor & Francis, 2012, ⟨10.1080/03081087.2012.716430⟩. ⟨inria-00610362v2⟩

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