Surfaces defined by pairs of polynomials
Algebraic Geometry
2025-09-12 v2
Abstract
We prove that the Brauer group of the generic diagonal surface of arbitrary degree is trivial. The same method is applied to surfaces whose equation can be written as the sum of two bilinear forms. This uses a general criterion for the triviality of the transcendental Brauer group of an isotrivial variety. We determine the field of definition of the geometric Picard group of the Fermat surface of arbitrary degree, thus finishing work of Shioda and Aoki.
Cite
@article{arxiv.2305.08632,
title = {Surfaces defined by pairs of polynomials},
author = {Damián Gvirtz-Chen and Alexei Skorobogatov},
journal= {arXiv preprint arXiv:2305.08632},
year = {2025}
}
Comments
32 pages, accepted for publication in Journal of the European Mathematical Society