On the Ideals of Secant Varieties of Segre Varieties

Authors:
J. M. Landsberg;L. Manivel
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA;Institut Fourier, UMR 5582 du CNRS, Université Grenoble I, BP 74 38402 Saint Martin d’Héres cedex, France
Venue:
Foundations of Computational Mathematics
Year:
2004

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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.