Quartic del Pezzo surfaces without quadratic points
| Autor: | Creutz, Brendan, Viray, Bianca |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$, and asked whether such surfaces always have a closed point of degree $2$. We resolve this by constructing infinitely many quartic del Pezzo surfaces over $\mathbb{Q}$ without degree $2$ points. These are the first examples of smooth intersections of two quadrics with index strictly less than the minimal degree of a closed point. Comment: 7 pages |
| Databáze: | arXiv |
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