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.
Kähler structures on spin 6-manifolds / S. Schreieder, L. Tasin. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 373:1/2(2019 Feb), pp. 397-419. [10.1007/s00208-017-1615-2]
Kähler structures on spin 6-manifolds
L. Tasin
2019
Abstract
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.File in questo prodotto:
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