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On deformations of ℚ-Fano threefolds II

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Published/Copyright: March 10, 2015
Journal für die reine und angewandte Mathematik
From the journal Journal für die reine und angewandte Mathematik Volume 2017 Issue 730

Abstract

We investigate some coboundary map associated to a 3-fold terminal singularity which is important in the study of deformations of singular 3-folds. We prove that this map vanishes only for quotient singularities and an A1,2/4-singularity, that is, a terminal singularity analytically isomorphic to a ℤ4-quotient of the singularity (x2+y2+z3+u2=0).

As an application, we prove that a ℚ-Fano 3-fold with terminal singularities can be deformed to one with only quotient singularities and A1,2/4-singularities. We also treat the ℚ-smoothability problem on ℚ-Calabi–Yau 3-folds.

Funding statement: The author is partially supported by Warwick Postgraduate Research Scholarship.

Acknowledgements

This paper is a part of the author’s Ph.D. thesis submitted to University of Warwick. The author would like to express deep gratitude to Professor Miles Reid for his warm encouragement and valuable comments. He would like to thank Professor Yoshinori Namikawa for useful conversations. Part of this paper is written during the author’s stay in Princeton University and the University of Tokyo. He would like to thank Professors János Kollár and Yujiro Kawamata for useful comments and nice hospitality. He thanks the referee for useful suggestions.

References

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Received: 2014-3-12
Revised: 2014-10-10
Published Online: 2015-3-10
Published in Print: 2017-9-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality
  3. Commuting-liftable subgroups of Galois groups II
  4. The hyperbolicity of the sphere complex via surgery paths
  5. Lefschetz properties for noncompact arithmetic ball quotients
  6. Plünnecke inequalities for countable abelian groups
  7. Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces
  8. On deformations of ℚ-Fano threefolds II
  9. K-theoretic duality for hyperbolic dynamical systems
https://doi.org/10.1515/crelle-2014-0125

Articles in the same Issue

  1. Frontmatter
  2. Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality
  3. Commuting-liftable subgroups of Galois groups II
  4. The hyperbolicity of the sphere complex via surgery paths
  5. Lefschetz properties for noncompact arithmetic ball quotients
  6. Plünnecke inequalities for countable abelian groups
  7. Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces
  8. On deformations of ℚ-Fano threefolds II
  9. K-theoretic duality for hyperbolic dynamical systems
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