Stable rationality in smooth families of threefolds

TL;DR

This paper demonstrates the existence of smooth projective threefold families where some fibers are stably rational while others are not, highlighting variability in rationality properties within a single family.

Contribution

It provides explicit examples of smooth threefold families with fibers exhibiting both stable rationality and non-stable rationality, advancing understanding of rationality in algebraic geometry.

Findings

Existence of families with mixed rationality properties

Explicit examples of smooth projective threefolds

Insights into stable rationality variability

Abstract

We exhibit families of smooth projective threefolds with both stably rational and non stably rational fibers.