On the rationality of quadric surface bundles

Abstract

For any standard quadric surface bundle over ${\mathbb{P}}^2$, we show that the locus of rational fibres is dense in the moduli space.

20 pages; to appear in Annales de l'Institut Fourier

References in corpus (4)

• On the rationality problem for quadric bundles
• Quadric surface bundles over surfaces and stable rationality
• Stable rationality of quadric and cubic surface bundle fourfolds
• Sums of three squares and Noether-Lefschetz loci