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Schreieder, Stefan; Tasin, Luca (2019): Kahler structures on spin 6-manifolds. In: Mathematische Annalen, Vol. 373, No. 1-2: pp. 397-419
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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.