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Partially Symmetric Tensors and the Non-defectivity of Secant Varieties of Products with a Projective Line as a Factor

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Abstract

We prove (with a mild restriction on the multidegrees) that all secant varieties of Segre–Veronese varieties with \(k>2\) factors, \(k-2\) of them being \(\mathbb {P}^1\), have the expected dimension. This is equivalent to compute the dimension of the set of all partially symmetric tensors with a fixed rank and the same format. The proof uses the case \(k=2\) proved by Galuppi and Oneto. Our theorem is an easy consequence of a theorem proved here for arbitrary projective varieties with a projective line as a factor and with respect to complete linear systems.

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Acknowledgements

The author is a member of GNSAGA of INdAM (Italy). We thanks a referee for helpful comments.

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  1. Department of Mathematics, University of Trento, Povo (TN), Trento, 38123, Italy

    Edoardo Ballico

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  1. Edoardo Ballico
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Ballico, E. Partially Symmetric Tensors and the Non-defectivity of Secant Varieties of Products with a Projective Line as a Factor. Vietnam J. Math. (2023). https://doi.org/10.1007/s10013-023-00670-y

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