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Bounding non-rationality of divisors on 3-fold Fano fibrations

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Veröffentlicht/Copyright: 14. August 2021
Journal für die reine und angewandte Mathematik (Crelles Journal)
Aus der Zeitschrift Journal für die reine und angewandte Mathematik (Crelles Journal) Band 2021 Heft 779

Abstract

In this paper we investigate non-rationality of divisors on 3-fold log Fano fibrations (X,B)→Z under mild conditions. We show that if D is a component of B with coefficient ≥t>0 which is contracted to a point on Z, then D is birational to ℙ1×C, where C is a smooth projective curve with gonality bounded depending only on t. Moreover, if t>12, then genus of C is bounded depending only on t.

Funding statement: The first author was supported by a grant of the Royal Society and did this work at the University of Cambridge. The second author was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project “5-100”, Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”, and the Simons Foundation.

Acknowledgements

The work on this paper was initiated while the second author visited the University of Cambridge. He thanks it for hospitality.

References

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Received: 2020-09-06
Revised: 2021-06-15
Published Online: 2021-08-14
Published in Print: 2021-10-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension
  3. On the rotational symmetry of 3-dimensional κ-solutions
  4. Automorphic ℒ‐invariants for reductive groups
  5. A p-adic variant of Kontsevich–Zagier integral operation rules and of Hrushovski–Kazhdan style motivic integration
  6. Harmonic branched coverings and uniformization of CAT(k) spheres
  7. Bounding non-rationality of divisors on 3-fold Fano fibrations
  8. Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces
  9. Milnor excision for motivic spectra
https://doi.org/10.1515/crelle-2021-0039

Artikel in diesem Heft

  1. Frontmatter
  2. Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension
  3. On the rotational symmetry of 3-dimensional κ-solutions
  4. Automorphic ℒ‐invariants for reductive groups
  5. A p-adic variant of Kontsevich–Zagier integral operation rules and of Hrushovski–Kazhdan style motivic integration
  6. Harmonic branched coverings and uniformization of CAT(k) spheres
  7. Bounding non-rationality of divisors on 3-fold Fano fibrations
  8. Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces
  9. Milnor excision for motivic spectra
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