All lines on a smooth cubic surface in terms of three skew lines
Algebraic Geometry
2022-09-01 v4
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 Schl\"afli's count of lines on real smooth cubic surfaces.
Cite
@article{arxiv.2002.10367,
title = {All lines on a smooth cubic surface in terms of three skew lines},
author = {Stephen McKean and Daniel Minahan and Tianyi Zhang},
journal= {arXiv preprint arXiv:2002.10367},
year = {2022}
}
Comments
21 pages, 5 figures, 1 table. Final version for journal