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The secant line variety to the varieties of reducible plane curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Catalisano, Maria Virginia Geramita, Anthony V. Gimigliano, Alessandro Shin, Yong-Su |
| Copyright Year | 2014 |
| Abstract | Let $$\lambda =[d_1,\ldots ,d_r]$$λ=[d1,…,dr] be a partition of $$d$$d. Consider the variety $$\mathbb {X}_{2,\lambda } \subset {\mathbb {P}}^N,\, N={d+2 \atopwithdelims ()2}-1$$X2,λ⊂PN,N=d+22-1, parameterizing forms $$F\in k[x_0,x_1,x_2]_d$$F∈k[x0,x1,x2]d which are the product of $$r\ge 2$$r≥2 forms $$F_1,\ldots ,F_r$$F1,…,Fr, with $$\deg F_i = d_i$$degFi=di. We study the secant line variety $$\sigma _2(\mathbb {X}_{2,\lambda })$$σ2(X2,λ), and we determine, for all $$r$$r and $$d$$d, whether or not such a secant variety is defective. Defectivity occurs in infinitely many “unbalanced” cases. |
| Starting Page | 423 |
| Ending Page | 443 |
| Page Count | 21 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10231-014-0470-y |
| Volume Number | 195 |
| Alternate Webpage(s) | https://www.usna.edu/Users/math/traves/halifax/Geramita.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1404.3911v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/1404.3911 |
| Alternate Webpage(s) | https://doi.org/10.1007/s10231-014-0470-y |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
