PreprintarXiv licencearXiv
General position on Brauer--Severi surfaces
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 Brauer--Severi 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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BibTeX
@misc{ritschel2026general,
title = {{General position on Brauer--Severi surfaces}},
author = {Jack Ritschel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.27940},
eprint = {2606.27940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27940},
}
RIS
TY - UNPB
TI - General position on Brauer--Severi surfaces
AU - Jack Ritschel
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2606.27940
UR - https://arxiv.org/abs/2606.27940
AB - 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 Brauer--Severi 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.
ER -