Intersections of three quadrics in $\mathbb{P}^7$

TL;DR

This paper investigates the rationality of smooth complete intersections of three quadrics in projective 7-space, demonstrating a family with both rational and non-rational examples.

Contribution

It provides the first explicit example of a family of such intersections exhibiting both rational and non-rational fibers.

Findings

Existence of a smooth family with both rational and non-rational fibers

Explicit examples illustrating rationality variation

Insights into the rationality problem for higher-dimensional intersections

Abstract

We study rationality properties of smooth complete intersections of three quadrics in $\mathbb{P}^7$. We exhibit a smooth family of such intersections with both rational and non-rational fibers.