Degree 2 del Pezzo surface bundles and stable rationality

2025/02/28 by Li, Wenhao
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.20761

Abstract

We study the arithmetic of del Pezzo surfaces Y of degree 2 over a function field, and in particular, the cokernel of the homomorphism from the Picard group to the Galois-invariants of the geometric Picard group Pic Y →(Pic Y)^G. Applying this to a fibration π:X→ S in del Pezzo surfaces of degree 2 over a rational surface S, we construct examples with nontrivial relative unramified cohomology group H²_nr,π(k(X)/k). A specialization argument implies the failure of stable rationality of varieties specializing to X.

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