Stable rationality of quadric surface bundles over surfaces

By Brendan Hassett, Alena Pirutka, Yuri Tschinkel. 2016

84 citations recorded by the source corpus.

We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both rational and non-rational fibers.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0fa767fda48207c64fab2f35a80164763f94a462

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In Geometry and Topology

1. Alexander Perry
2. Johannes Nicaise
3. Evgeny Shinder
4. M. Temkin
5. L. H. Halle
6. Alexander Kuznetsov

Citations in the corpus

• The motivic nearby fiber and degeneration of stable rationality (2017, background): “e general statement. On the other hand, it is known that rationality and stable rationality are not open properties: there exist examples where Sis connected and Ssr is a non-empty strict subset of S [HPT18]. The theorem also explains why in practice, for a given smooth family of varieties, proving ”
• 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.”