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arXiv · 2002.10367

All lines on a smooth cubic surface in terms of three skew lines

Stephen McKean·Daniel Minahan·Tianyi Zhang
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Abstract

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 Schläfli's count of lines on real smooth cubic surfaces.

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Stephen McKean, Daniel Minahan, Tianyi Zhang. 2021-07-15. All lines on a smooth cubic surface in terms of three skew lines. https://arxiv.org/abs/2002.10367

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