The count of quadratic point pairs on the non-split quadrics x^2 - d y^2 = z w matches the predicted c B log B, once a thin set of new flavour (contributing the same order) is removed.
Quartic del Pezzo surfaces without quadratic points
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
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 $\mathbb{Q}$ 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.
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Counting quadratic points on Fano varieties
The count of quadratic point pairs on the non-split quadrics x^2 - d y^2 = z w matches the predicted c B log B, once a thin set of new flavour (contributing the same order) is removed.