Stable rationality in smooth families of threefolds
Brendan Hassett, Andrew Kresch, Yuri Tschinkel

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.
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