Mathematische Annalen

, Volume 373, Issue 1–2, pp 397–419 | Cite as

Kähler structures on spin 6-manifolds

  • Stefan SchreiederEmail author
  • Luca Tasin


We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kähler manifold. Moreover, for given Betti numbers, there are only finitely many deformation types and hence topological types of smooth complex projective spin threefolds of general type. Finally, on a fixed spin 6-manifold, the Chern numbers take on only finitely many values on all possible Kähler structures.

Mathematics Subject Classification

Primary 14F45 32Q15 57R15 Secondary 14E30 57R20 



The first author is member of the SFB/TR 45. During parts of this project, the second author was supported by the DFG Emmy Noether-Nachwuchsgruppe “Gute Strukturen in der höherdimensionalen birationalen Geometrie” and thereby also member of the SFB/TR 45. We thank D. Kotschick for detailed comments and P. Cascini, M. Land, E. Sernesi, R. Svaldi and B. Totaro for conversations.


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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Mathematisches Institut, LMU MünchenMünchenGermany
  2. 2.Mathematical Institute of the University of BonnBonnGermany

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