Conics meeting eight lines over perfect fields
Algebraic Geometry
2023-06-01 v2
Abstract
Over the complex numbers, there are 92 plane conics meeting 8 general lines in projective 3-space. Using the Euler class and local degree from motivic homotopy theory, we give an enriched version of this result over any perfect field. This provides a weighted count of the number of plane conics meeting 8 general lines, where the weight of each conic is determined the geometry of its intersections with the 8 given lines. As a corollary, real conics meeting 8 general lines come in two families of equal size.
Keywords
Cite
@article{arxiv.2107.05543,
title = {Conics meeting eight lines over perfect fields},
author = {Cameron Darwin and Aygul Galimova and Miao Pam Gu and Stephen McKean},
journal= {arXiv preprint arXiv:2107.05543},
year = {2023}
}
Comments
20 pages. Revised version with various errors corrected. Final version, but comments still welcome!