On integral points on degree four del Pezzo surfaces

2016/02/09 by Jahnel, Jörg, Schindler, Damaris
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1602.03118

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.

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