Papers › Quartic del Pezzo surfaces without quadratic points
Quartic del Pezzo surfaces without quadratic points
Brendan Creutz, Bianca Viray
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Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$ (i.e., has a closed point of degree $2$ modulo $4$),, 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 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.
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