On integral points on degree four del Pezzo surfaces

Joerg Jahnel; Damaris Schindler

doi:10.1007/s11856-017-1581-0

On integral points on degree four del Pezzo surfaces

Joerg Jahnel
, Damaris Schindler

Research output: Contribution to journal › Article › Academic › peer-review

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 and over p for all primes p, but not over. By blow-up, these yield cubic polynomials in three variables all integral solutions of which satisfy a gcd condition.

Original language	English
Pages (from-to)	21-62
Number of pages	42
Journal	Israel Journal of Mathematics
Volume	222
Issue number	1
DOIs	https://doi.org/10.1007/s11856-017-1581-0
Publication status	Published - Oct 2017

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10.1007%2Fs11856-017-1581-0Final published version, 466 KBLicence: Taverne

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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 and over p for all primes p, but not over. By blow-up, these yield cubic polynomials in three variables all integral solutions of which satisfy a gcd condition. ",

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AB - 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 and over p for all primes p, but not over. By blow-up, these yield cubic polynomials in three variables all integral solutions of which satisfy a gcd condition.

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DO - 10.1007/s11856-017-1581-0

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JO - Israel Journal of Mathematics

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On integral points on degree four del Pezzo surfaces

Abstract

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