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On integral points on open degree four del Pezzo surfaces

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Date: Thursday, January 28, 2021 14:00 - 15:00
Speaker: Jörg Jahnel (University of Siegen)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tim Browning

I will report on investigations, joint with Damaris Schindler (Göttingen), concerning the 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 $\bbQ$ and over $\bbZ_p$ for all primes $p$, but not over $\bbZ$. By blow-up, these yield cubic polynomials in three variables all integral solutions of which satisfy a gcd condition.


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