Weak weak approximation for certain quadric surface bundles

TL;DR

This paper studies the weak approximation property for specific quadric surface bundles, focusing on cases that relate to recent research by Hassett, Pirutka, and Tschinkel, with a focus on arithmetic geometry.

Contribution

It establishes weak approximation results for certain biquadratic fourfolds, extending understanding of rational points on these algebraic varieties.

Findings

Weak approximation holds away from a finite set of places for these fourfolds.

Connections made to recent work by Hassett, Pirutka, and Tschinkel.

Provides new insights into the arithmetic of quadric surface bundles.

Abstract

We investigate weak approximation away from a finite set of places for a class of biquadratic fourfolds inside $\mathbb{P}^3 \times \mathbb{P}^2$, some of which appear in the recent work of Hassett--Pirutka--Tschinkel.