English

Brauer groups of certain affine cubic surfaces

Algebraic Geometry 2025-10-30 v2 Number Theory

Abstract

We study the Brauer groups of affine surfaces that are complements of singular hyperplane sections of smooth cubic surfaces over a field kk of characteristic 00. We determine the Brauer group over the algebraic closure as a Galois module for all the possible singular hyperplane sections. For the case when the hyperplane section is geometrically the union of three lines, we give explicit examples where transcendental elements of order 22 and 33 exist over Q\mathbb{Q}. We end with an application on the integral Brauer-Manin obstruction to the integral Hasse principle.

Keywords

Cite

@article{arxiv.2509.16042,
  title  = {Brauer groups of certain affine cubic surfaces},
  author = {Abdulmuhsin Alfaraj},
  journal= {arXiv preprint arXiv:2509.16042},
  year   = {2025}
}
R2 v1 2026-07-01T05:45:56.975Z