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arXiv · 1404.3911

The secant line variety to the varieties of reducible plane curves

Maria Virginia Catalisano·Anthony V. Geramita·Alessandro Gimigliano·Yong-Su Shin
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Abstract

Let $λ=[d_1,\dots,d_r]$ be a partition of $d$. Consider the variety $\mathbb{X}_{2,λ} \subset \mathbb{P}^N$, $N={d+2 \choose 2}-1$, 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 $σ_2(\mathbb{X}_{2,λ})$, and we determine, for all $r$ and $d$, whether or not such a secant variety is defective. Defectivity occurs in infinitely many "unbalanced" cases.

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Maria Virginia Catalisano, Anthony V. Geramita, Alessandro Gimigliano, Yong-Su Shin. 2014-11-28. The secant line variety to the varieties of reducible plane curves. https://arxiv.org/abs/1404.3911

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