Kähler structures on spin 6-manifolds
2019
We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kahler 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 Kahler structures.
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