Weak approximation on del Pezzo surfaces of degree 1
Number Theory
2009-01-08 v2 Algebraic Geometry
Abstract
We study del Pezzo surfaces of degree 1 of the form w^2 = z^3 + Ax^6 + By^6 in the weighted projective space P_k(1,1,2,3), where k is a perfect field of characteristic not 2 or 3 and A,B \in k^*. Over a number field, we exhibit an infinite family of (minimal) counterexamples to weak approximation amongst these surfaces, via a Brauer-Manin obstruction.
Keywords
Cite
@article{arxiv.0801.2430,
title = {Weak approximation on del Pezzo surfaces of degree 1},
author = {Anthony Várilly-Alvarado},
journal= {arXiv preprint arXiv:0801.2430},
year = {2009}
}
Comments
20 pages, no figures, Latex. Introduction revised to highlight Theorem 3.3; typos corrected. Magma scripts included at end of sourcefile