On the Ideals of Secant Varieties of Segre Varieties
نویسندگان
چکیده
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.
منابع مشابه
On the Ideals and Singularities of Secant Varieties of Segre Varieties
We find minimal generators for the ideals of secant varieties of Segre varieties in the cases of σk(P 1 × P n × P ) for all k, n,m, σ2(P n × P m × P p × P ) for all n,m, p, r (GSS conjecture for four factors), and σ3(P n ×P m ×P ) for all n,m, p and prove they are normal with rational singularities in the first case and arithmetically Cohen-Macaulay in the second two.
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ورودعنوان ژورنال:
- Foundations of Computational Mathematics
دوره 4 شماره
صفحات -
تاریخ انتشار 2004