On integral points on degree four del Pezzo surfaces
Number Theory
2017-07-28 v4 Algebraic Geometry
Abstract
We report on our investigations concerning algebraic and transcendental Brauer-Manin obstructions to integral points on complements of a hyperplane section in degree four del Pezzo surfaces. We discuss moreover two concepts of an obstruction at an archimedean place. Concrete examples are given of pairs of non-homogeneous quadratic polynomials in four variables representing (0,0) over Q and over Z_p for all primes p, but not over Z. By blow-up, these yield cubic polynomials in three variables all integral solutions of which satisfy a gcd condition.
Cite
@article{arxiv.1602.03118,
title = {On integral points on degree four del Pezzo surfaces},
author = {Jörg Jahnel and Damaris Schindler},
journal= {arXiv preprint arXiv:1602.03118},
year = {2017}
}
Comments
39 pages