Group Actions on S^6 and complex structures on P_3
Abstract
It is proved that if S^6 possesses an integrable complex structure, then there exists a 1dimensional family of pairwise different exotic complex structures on P_3(C). This follows immediately from the main result of the paper: S^6 is not the underlying differentiable manifold of an almost homogeneous complex manifold X. Via elementary Lie theoretic techniques this is reduced to ruling out the possibility of a C^*action on a certain nonnormal surface E in X. A contradiction is reached by analyzing combinatorial aspects of the nonnormal locus N of E and its preimage in the normalization of E.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1998
 arXiv:
 arXiv:math/9812076
 Bibcode:
 1998math.....12076H
 Keywords:

 Algebraic Geometry;
 Differential Geometry;
 53C15;
 32C10;
 32M12