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arxiv: math/0311388 · v1 · submitted 2003-11-21 · 🧮 math.AG · math.RT

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On the ideals of secant varieties of Segre varieties

J.M. Landsberg , Laurent Manivel
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classification 🧮 math.AG math.RT
keywords varietiessecantidealsconjecturefactorssegresolvearbitrary
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We establish basic techniques for studying 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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