On non-defectivity of certain Segre-Veronese varieties

被引：17

作者：

Abo, Hirotachi ^{[1
]}

机构：

[1] Univ Idaho, Dept Math, Moscow, ID 83844 USA

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2010年 / 45卷 / 12期

基金：

美国国家科学基金会;

关键词：

Secant varieties; Segre-Veronese varieties; Non-defectivity; SECANT VARIETIES;

D O I：

10.1016/j.jsc.2010.06.008

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Let X(m,n) be the Segre-Veronese variety P(m) x P(n) embedded by the morphism given by O(1,2) and let sigma(s)(X(m,n)) denote the sth secant variety of X(m,n). In this paper, we prove that if m = n or m = n + 1, then sigma(s)(X(m,n)) has the expected dimension except for sigma(6)(X(4,3)). As an immediate consequence, we will give functions s(1)(m, n) <= s(2)(m, n) such that if s <= s(1) (m, n) or if s >= s(2)(m, n), then sigma(s)(X(m,n)) has the expected dimension for all positive integers m and n. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1254 / 1269

页数：16