On the rationality problem for quadric bundles
By Stefan Schreieder. Duke mathematical journal, 2017
46 citations recorded by the source corpus.
We classify all positive integers n and r such that (stably) non-rational complex r-fold quadric bundles over rational n-folds exist. We show in particular that for any n and r, a wide class of smooth r-fold quadric bundles over projective n-space are not stably rational if r lies in the interval from $2^{n-1}-1$ to $2^{n}-2$. In our proofs we introduce a generalization of the specialization method of Voisin and Colliot-Th\'el\`ene--Pirutka which avoids universally $CH_0$-trivial resolutions of singularities.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a317e05a32a4df4e8858355241e61d63e251e37d
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- The integral Hodge conjecture for two-dimensional Calabi–Yau categories (2020, background): “This jibes with the fact that, despite many recent advances on the rationality problem [91, 18, 86, 34, 77, 78, 74, 49], irrationality results remain out of reach for such fourfolds.”