Conics meeting eight lines over perfect fields
| Autor: | Cameron Darwin, Aygul Galimova, Miao (Pam) Gu, Stephen McKean |
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| Rok vydání: | 2021 |
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| DOI: | 10.48550/arxiv.2107.05543 |
| Popis: | 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. Comment: 20 pages. Revised version with various errors corrected. Final version, but comments still welcome! |
| Databáze: | OpenAIRE |
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