2023/11/30 by Pirutka, Alena
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.00144
In this note we define a subgroup Hinr,π of unramified cohomology group Hinr of a fibration π:X→ S. This subgroup can be used efficiently in refined specialization arguments and allows to detect the failure of stable rationality of a variety specializing to X. We compute H2nr, π systematically for many cubic surface bundles π:X→ S over a smooth projective rational surface over an algebraically closed field: we give a combinatorial formula in terms of components of the discriminant divisor of π.