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arXiv · 2606.27940

General position on Severi--Brauer surfaces

Jack Ritschel
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Abstract

The blowing-up of the projective plane at a finite set of points yields a del Pezzo surface if and only if the points lie in general position. In this note, we generalize this result to Severi--Brauer surfaces over arbitrary ground fields. Using Galois descent, intersection theory and combinatorial arguments, we provide explicit arithmetic and geometric conditions on the centre of the blowing-up.

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Jack Ritschel. 2026-06-26. General position on Severi--Brauer surfaces. https://arxiv.org/abs/2606.27940

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