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.
متن کاملSecant Varieties of Toric Varieties
If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...
متن کاملSecant varieties
The goal of this talk is to introduce secant varieies and show connections of secant varieties of Veronese variety to the Waring problem. 1 Secant varieties Let X ⊂ P be a variety over k, where k is algebraically closed field of characteristic 0 (or just assume k = C). Definition 1.1. For s ≥ 1 the s-th higher secant variety of X is
متن کاملGrassmannians of Secant Varieties
For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec k (X), for 0 < h < k. These families have an expected dimension and we study varieties for which the expected dimension is not attained; for these varieties, making general consecutive projections to lower dimensional spaces, we do not get the expected singularities. In particular, we ex...
متن کاملSecant Varieties of Segre-veronese Varieties
In this paper we study the dimension of secant varieties of Segre-Veronese varieties P × P embedded by the morphism given by O(1, 2). Given the dimensions m, n, we provide two functions s(m, n) and s(m, n), such that the s secant variety is nondefective, i.e. it has the expected dimension, if s ≤ s(m, n) or s ≥ s(m, n). Finally, we present a conjecturally complete list of defective secant varie...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2017
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnw321