Secant Varieties of Segre-veronese Varieties
نویسنده
چکیده
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 varieties of such Segre-Veronese varieties.
منابع مشابه
New Examples of Defective Secant Varieties of Segre-veronese Varieties
We prove the existence of defective secant varieties of three-factor and four-factor Segre-Veronese varieties embedded in certain multi-degree. These defective secant varieties were previously unknown and are of importance in the classification of defective secant varieties of Segre-Veronese varieties with three or more factors.
متن کاملOn the Secant Defectivity of Segre-veronese Varieties
Let X ⊆ PN be a non-degenerate projective variety of dimension d. Then the sth secant variety of X, denoted σs(X), is the Zariski closure of the union of linear spans of s-tuples of points lying on X. The study of secant varieties has a long history. The interest in this subject goes back to the Italian school at the turn of the 20th century. This topic has received renewed interest over the pa...
متن کاملSecant Varieties of Segre-Veronese Varieties Pm × Pn Embedded by O(1, 2)
Let Xm,n be the Segre-Veronese variety P m ×P embedded by the morphism given by O(1, 2). In this paper, we provide two functions s(m, n) ≤ s(m, n) such that the s secant variety of Xm,n has the expected dimension if s ≤ s(m,n) or s(m, n) ≤ s. We also present a conjecturally complete list of defective secant varieties of such Segre-Veronese varieties.
متن کاملTensor Ranks on Tangent Developable of Segre Varieties
We describe the stratification by tensor rank of the points belonging to the tangent developable of any Segre variety. We give algorithms to compute the rank and a decomposition of a tensor belonging to the secant variety of lines of any Segre variety. We prove Comon’s conjecture on the rank of symmetric tensors for those tensors belonging to tangential varieties to Veronese varieties.
متن کامل