Hodge numbers of a hypothetical complex structure on the six sphere (Q1580270)

From author's abstract: The author proves that the terms \(E_r^{p,q} (S^6)\) in the Frölicher spectral sequence associated to any hypothetical complex structure on \(S^6\) would satisfy Serre duality. It is also shown that the vanishing of the Dolbeault cohomology group \(H^{1,1}(S^6)\) ensures the existence of a holomorphic 2-form on \(S^6\) living even in \(E^{2,0}_2 (S^6)\), which in particular implies the nondegeneration of Frölicher's sequence at the second level.