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Tangential varieties of Segre–Veronese varieties

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


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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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Correspondence to Claudiu Raicu.

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Oeding, L., Raicu, C. Tangential varieties of Segre–Veronese varieties. Collect. Math. 65, 303–330 (2014).

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