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Hodge numbers of a hypothetical complex structure on \(S^{6}\). (English) Zbl 1387.32033
Summary: These are the notes for the talk “Hodge numbers of a hypothetical complex structure on \(S^6\)” given by the author at the MAM1 “(Non)-existence of complex structures on \(S^6\)” held in Marburg in March 2017. They are based on [A. Gray, Boll. Unione Mat. Ital., VII. Ser., B 11, No. 2, Suppl., 251–255 (1997; Zbl 0891.53018); L. Ugarte, Geom. Dedicata 81, No. 1–3, 173–179 (2000; Zbl 0996.53046)], where Hodge numbers and the dimensions of the successive pages of the Frölicher spectral sequence for \(S^6\) endowed with a hypothetical complex structure are investigated. We also add results from [A. P. McHugh, Eur. J. Pure Appl. Math. 10, No. 3, 440–454 (2017; Zbl 1366.53053)], where the Bott-Chern cohomology of hypothetical complex structures on \(S^6\) is studied. The material is not intended to be original.

MSC:
32Q99 Complex manifolds
32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
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