On stable rationality of Fano threefolds and del Pezzo fibrations
Brendan Hassett, Yuri Tschinkel
TL;DR
This paper proves that most non-rational Fano threefolds, which are not birational to cubic threefolds, are also not stably rational, advancing understanding of their rationality properties.
Contribution
It establishes the stable non-rationality of very general non-rational Fano threefolds excluding those birational to cubic threefolds.
Findings
Most non-rational Fano threefolds are not stably rational.
Fano threefolds not birational to cubic threefolds are proven to be stably non-rational.
The result narrows the classification of rationality for Fano threefolds.
Abstract
We prove that very general non-rational Fano threefolds which are not birational to cubic threefolds are not stably rational.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Geometry and complex manifolds