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On the ideals of secant varieties of Segre varieties. (English) Zbl 1068.14068
The authors develop here several basic techniques for determining the homogeneous ideal of the secant varieties of Segre varieties. They apply their techniques in several examples. In particular they give an affirmative answer to a conjecture of L. D. Garcia, M. Stillman and B. Sturmfels [Algebraic geometry of Bayesian networks, preprint, http://arXiv.org/abs/math.AG/0301255] on the generators of the homogeneous ideal in the case of three factors and set-theoretically for an arbitrary number of factors.

MSC:
14Q15 Computational aspects of higher-dimensional varieties
14N05 Projective techniques in algebraic geometry
14M17 Homogeneous spaces and generalizations
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