New Examples of Defective Secant Varieties of Segre-veronese Varieties
نویسنده
چکیده
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.
منابع مشابه
On 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
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...
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 کاملHIGHER SECANT VARIETIES OF P n × P m EMBEDDED IN BI - DEGREE (
Let X (n,m) (1,d) denote the Segre-Veronese embedding of Pn×Pm via the sections of the sheaf O(1, d). We study the dimensions of higher secant varieties of X (n,m) (1,d) and we prove that there is no defective sth secant variety, except possibly for n values of s. Moreover when (m+d d ) is a multiple of (m+ n+ 1), the sth secant variety of X (n,m) (1,d) has the expected dimension for every s.
متن کامل