On integral points on degree four del Pezzo surfaces
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 Zp 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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