Vertical Brauer groups and del Pezzo surfaces of degree 4
Algebraic Geometry
2013-06-05 v3 Number Theory
Abstract
We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical for some projection away from a plane f: X ---> P^1, i.e., that every Brauer class is obtained by pullback from an element of Br k(P^1). As a consequence, we prove that a Brauer class does not obstruct the existence of a rational point if and only if there exists a fiber of f that is locally solvable. The proof is constructive and gives a simple and practical algorithm, distinct from that in [BBFL07], for computing all classes in the Brauer group of X (modulo constant algebras).
Keywords
Cite
@article{arxiv.1210.0920,
title = {Vertical Brauer groups and del Pezzo surfaces of degree 4},
author = {Anthony Várilly-Alvarado and Bianca Viray},
journal= {arXiv preprint arXiv:1210.0920},
year = {2013}
}
Comments
Added sections 4.2.1 and 5.5. Introduction modified accordingly. Code scripts available in the source submission