Degree 2 del Pezzo surface bundles and stable rationality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929735384170496 |
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| author | Li, Wenhao |
| author_facet | Li, Wenhao |
| contents | 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 $\operatorname{Pic} Y \rightarrow(\operatorname{Pic} \bar{Y})^{G}$. Applying this to a fibration $π:X\to S$ in del Pezzo surfaces of degree 2 over a rational surface $S$, we construct examples with nontrivial relative unramified cohomology group $H^2_{nr,π}(k(X)/k)$. A specialization argument implies the failure of stable rationality of varieties specializing to $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degree 2 del Pezzo surface bundles and stable rationality Li, Wenhao Algebraic Geometry 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 $\operatorname{Pic} Y \rightarrow(\operatorname{Pic} \bar{Y})^{G}$. Applying this to a fibration $π:X\to S$ in del Pezzo surfaces of degree 2 over a rational surface $S$, we construct examples with nontrivial relative unramified cohomology group $H^2_{nr,π}(k(X)/k)$. A specialization argument implies the failure of stable rationality of varieties specializing to $X$. |
| title | Degree 2 del Pezzo surface bundles and stable rationality |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.20761 |