Completions of affine spaces into Mori fiber spaces with non-rational fibers

TL;DR

This paper introduces a method to complete affine spaces into Mori fiber spaces over the projective line, producing examples with non-rational, birationally rigid, and non-stably rational fibers, advancing understanding of their structure.

Contribution

It presents a novel construction technique for Mori fiber spaces with non-rational fibers, expanding the class of known examples and their properties.

Findings

Constructed families of Mori fiber spaces with non-rational fibers

Demonstrated birational rigidity of the fibers

Showed fibers are not stably rational

Abstract

We describe a method to construct completions of affine spaces into total spaces of $\mathbb{Q}$-factorial terminal Mori fiber spaces over the projective line. As an application we provide families of examples with non-rational, birationally rigid and non-stably rational general fibers.