The secant line variety to the varieties of reducible plane curves

被引：7

作者：

Catalisano, Maria Virginia ^{[1
]}

Geramita, Anthony V. ^{[2
,3
]}

Gimigliano, Alessandro ^{[4
]}

Shin, Yong-Su ^{[5
]}

机构：

[1] Univ Genoa, Dipartimento Ingn Meccan Energet Gest & Trasporti, Genoa, Italy

[2] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

[3] Univ Genoa, Dipartimento Matemat, Genoa, Italy

[4] Univ Bologna, Dipartmento Matemat, Bologna, Italy

[5] Sungshin Womens Univ, Dept Math, Seoul 136742, South Korea

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2016年 / 195卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Secant variety; Reducible plane curves; Defectivity; STAR-CONFIGURATION; POINTS;

D O I：

10.1007/s10231-014-0470-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let lambda = [d(1),..., d(r)] be a partition of d. Consider the variety X-2,X-lambda subset of P-N, N = ((d+ 2)(2)) - 1, parameterizing forms F is an element of k[ x(0), x(1), x(2)](d) which are the product of r >= 2 forms F-1,..., F-r, with deg F-i = d(i). We study the secant line variety sigma(2)(X-2,X-lambda), and we determine, for all r and d, whether or not such a secant variety is defective. Defectivity occurs in infinitely many "unbalanced" cases.

引用

页码：423 / 443

页数：21

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