1998/12/13 by Alan T. Huckleberry, Alan Huckleberry, Stefan Kebekus +4
Mathematics · #32C10 #32M12 #53C15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.DG #msc:32C10 #msc:32M12 #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/9812076
arxiv created 1998/12/13 · openalex publication_date 1998/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is proved that if S6 possesses an integrable complex structure, then there exists a 1-dimensional family of pairwise different exotic complex structures on P3(C). This follows immediately from the main result of the paper: S6 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.