Group Actions on S^6 and complex structures on P_3
代数几何
2007-05-23 v1 微分几何
摘要
It is proved that if S^6 possesses an integrable complex structure, then there exists a 1-dimensional 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 non-normal surface E in X. A contradiction is reached by analyzing combinatorial aspects of the non-normal locus N of E and its preimage in the normalization of E.
引用
@article{arxiv.math/9812076,
title = {Group Actions on S^6 and complex structures on P_3},
author = {Alan T. Huckleberry and Stefan Kebekus and Thomas Peternell},
journal= {arXiv preprint arXiv:math/9812076},
year = {2007}
}