Grassmannians of secant varieties

被引：27

作者：

Chiantini, L

Coppens, M

机构：

[1] Univ Siena, Dipartimento Matemat, I-53100 Siena, Italy

[2] Katholieke Hogesch Kempen, Dept Ind Ingenieur & Biotech, B-2440 Geel, Belgium

来源：

FORUM MATHEMATICUM | 2001年 / 13卷 / 05期

关键词：

D O I：

10.1515/form.2001.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an irreducible projective variety X, we study the family of h-planes contained in the secant variety S-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 examine the family G(1,2) of lines sitting in 3-secant planes to a surface S. We show that the actual dimension of G(1,2) is equal to the expected dimension unless S is a cone or a rational normal scroll of degree 4 in P-5.

引用

页码：615 / 628

页数：14