Unbounded negativity on rational surfaces in positive characteristic
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Raymond Cheng
und
Remy van Dobben de Bruyn
Abstract
We give explicit blowups of the projective plane in positive characteristic that contain smooth rational curves of arbitrarily negative self-intersection, showing that the Bounded Negativity Conjecture fails even for rational surfaces in positive characteristic. As a consequence, we show that any surface in positive characteristic admits a birational model failing the Bounded Negativity Conjecture.
Funding statement: Remy van Dobben de Bruyn was partly supported by the Oswald Veblen Fund at the Institute for Advanced Study.
Acknowledgements
We thank Johan de Jong, Joaquín Moraga, Takumi Murayama, Will Sawin, and John Sheridan for helpful discussions, and we thank the referee for suggestions to streamline the exposition.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- An explicit formula for the Siegel series of a quadratic form over a non-archimedean local field
- Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case)
- Prescribing Ricci curvature on homogeneous spaces
- Self-similar solutions to fully nonlinear curvature flows by high powers of curvature
- Ricci flow on manifolds with boundary with arbitrary initial metric
- Unbounded negativity on rational surfaces in positive characteristic
- Extending torsors on the punctured Spec(Ainf)
- Non-isomorphic 2-groups with isomorphic modular group algebras
- Erratum to Profinite rigidity for twisted Alexander polynomials (J. reine angew. Math. 771 (2021), 171–192)
Artikel in diesem Heft
- Frontmatter
- An explicit formula for the Siegel series of a quadratic form over a non-archimedean local field
- Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case)
- Prescribing Ricci curvature on homogeneous spaces
- Self-similar solutions to fully nonlinear curvature flows by high powers of curvature
- Ricci flow on manifolds with boundary with arbitrary initial metric
- Unbounded negativity on rational surfaces in positive characteristic
- Extending torsors on the punctured Spec(Ainf)
- Non-isomorphic 2-groups with isomorphic modular group algebras
- Erratum to Profinite rigidity for twisted Alexander polynomials (J. reine angew. Math. 771 (2021), 171–192)
