On integral points on degree four del Pezzo surfaces |
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Authors: | Jörg Jahnel Damaris Schindler |
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Institution: | 1.Département Mathematik,Universit?t Siegen,Siegen,Germany;2.Mathematical Institute,Universiteit Utrecht,Utrecht,Netherlands |
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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 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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