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arXiv · 2107.05543

Conics meeting eight lines over perfect fields

Cameron Darwin·Aygul Galimova·Miao Pam Gu·Stephen McKean
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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.

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Cameron Darwin, Aygul Galimova, Miao Pam Gu, Stephen McKean. 2021-07-12. Conics meeting eight lines over perfect fields. https://doi.org/10.1016/j.jalgebra.2023.04.024

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