%0 Journal Article
%T The secant line variety to the varieties of reducible plane curves
%A Maria Virginia Catalisano
%A Anthony V. Geramita
%A Alessandro Gimigliano
%A Yong-Su Shin
%J Mathematics
%D 2014
%I arXiv
%X Let $\lambda =[d_1,\dots,d_r]$ be a partition of $d$. Consider the variety $\mathbb{X}_{2,\lambda} \subset \mathbb{P}^N$, $N={d+2 \choose 2}-1$, parameterizing forms $F\in k[x_0,x_1,x_2]_d$ which are the product of $r\geq 2$ forms $F_1,\dots,F_r$, with deg$F_i = d_i$. We study the secant line variety $\sigma_2(\mathbb{X}_{2,\lambda})$, and we determine, for all $r$ and $d$, whether or not such a secant variety is defective. Defectivity occurs in infinitely many "unbalanced" cases.
%U http://arxiv.org/abs/1404.3911v2