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On the Ideals of Secant Varieties of Segre Varieties

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Abstract

We establish basic techniques for determining the ideals of secant varieties of Segre varieties.We solve a conjecture of Garcia, Stillman, and Sturmfels on the generators of the ideal of the first secant variety in the case of three factors and solve the conjecture set-theoretically for an arbitrary number of factors. We determine the low degree components of the ideals of secant varieties of small dimension in a few cases.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA

    J. M. Landsberg

  2. Institut Fourier, UMR 5582 du CNRS, Université Grenoble I, BP 74 38402 Saint Martin d’Héres cedex, France

    L. Manivel

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  1. J. M. Landsberg
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  2. L. Manivel
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Correspondence to J. M. Landsberg or L. Manivel.

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Landsberg, J., Manivel, L. On the Ideals of Secant Varieties of Segre Varieties. Found Comput Math 4, 397–422 (2004). https://doi.org/10.1007/s10208-003-0115-9

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  • DOI: https://doi.org/10.1007/s10208-003-0115-9

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