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Tangential varieties of Segre–Veronese surfaces are never defective

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Abstract

We compute the dimensions of all the secant varieties to the tangential varieties of all Segre–Veronese surfaces. We exploit the typical approach of computing the Hilbert function of special 0-dimensional schemes on projective plane by using a new degeneration technique.

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Acknowledgements

The first author was supported by the Università degli Studi di Genova through the “FRA (Fondi per la Ricerca di Ateneo) 2015”. The second author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445).

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Authors and Affiliations

  1. Dipartimento di Ingegneria Meccanica, Energetica, Gestionale e dei Trasporti, Universita degli studi di Genova, Genoa, Italy

    Maria Virginia Catalisano

  2. Barcelona Graduate School of Mathematics (BGSMath) and Department of Mathematics, Universitat Politecnica de Catalunya, Barcelona, Spain

    Alessandro Oneto

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  1. Maria Virginia Catalisano
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  2. Alessandro Oneto
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Correspondence to Alessandro Oneto.

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Catalisano, M.V., Oneto, A. Tangential varieties of Segre–Veronese surfaces are never defective. Rev Mat Complut 33, 295–324 (2020). https://doi.org/10.1007/s13163-019-00305-2

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