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Tangential varieties of Segre–Veronese varieties

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Abstract

We determine the minimal generators of the ideal of the tangential variety of a Segre–Veronese variety, as well as the decomposition into irreducible \({GL}\)-representations of its homogeneous coordinate ring. In the special case of a Segre variety, our results confirm a conjecture of Landsberg and Weyman.

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Notes

  1. For convenience we dualize vector spaces here so that our modules of polynomials may be written without the dual.

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Acknowledgments

We would like to thank J. M. Landsberg, Giorgio Ottaviani, and Bernd Sturmfels for useful suggestions, as well as the anonymous referee for many valuable comments. The Macaulay2 algebra software [10] was helpful in many experiments, particularly through the SchurRings package [18] which was used to predict some of the syzygy functors described in the paper. The second author was partially supported by the National Science Foundation Grant No. 1303042.

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Author notes

  1. Luke Oeding

    Present address: Department of Mathematics and Statistics Auburn University, Auburn, AL, 36849-5310, USA

Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA , 94720-3840, USA

    Luke Oeding

  2. Department of Mathematics, Princeton University, Princeton, NJ , 08544-1000, USA

    Claudiu Raicu

  3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania

    Claudiu Raicu

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  1. Luke Oeding
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  2. Claudiu Raicu
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Correspondence to Claudiu Raicu.

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Oeding, L., Raicu, C. Tangential varieties of Segre–Veronese varieties. Collect. Math. 65, 303–330 (2014). https://doi.org/10.1007/s13348-014-0111-1

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