All lines on a smooth cubic surface in terms of three skew lines
| Autor: | McKean, Stephen, Minahan, Daniel, Zhang, Tianyi |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | New York J. Math. 27(1), 1305 -- 1327 (2021) |
| Druh dokumentu: | Working Paper |
| Popis: | Jordan showed that the incidence variety of a smooth cubic surface containing 27 lines has solvable Galois group over the incidence variety of a smooth cubic surface containing 3 skew lines. As noted by Harris, it follows that for any smooth cubic surface, there exist formulas for all 27 lines in terms of any 3 skew lines. In response to a question of Farb, we compute these formulas explicitly. We also discuss how these formulas relate to Schl\"afli's count of lines on real smooth cubic surfaces. Comment: 21 pages, 5 figures, 1 table. Final version for journal |
| Databáze: | arXiv |
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