Rationality does not specialize among terminal fourfolds

TL;DR

This paper proves that rationality is not a property that necessarily persists in flat families of complex fourfolds with terminal singularities, filling a gap in the understanding of rationality behavior in algebraic geometry.

Contribution

It demonstrates that rationality does not specialize among terminal fourfolds, extending Totaro's earlier results to the four-dimensional case.

Findings

Rationality does not necessarily persist in flat families of fourfolds.

The result fills a gap in the understanding of rationality in algebraic geometry.

It confirms that rationality behavior in fourfolds differs from higher dimensions.

Abstract

We show that rationality does not specialize in flat projective families of complex fourfolds with terminal singularities. This answers a question of Totaro, who established the analogous result in all dimensions greater than 4.