2018/07/19 by Hong, Jaehyun, Huckleberry, Alan, Seo, Aeryeong
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1807.07311
A real semisimple Lie group G0 embedded in its complexification G has only finitely many orbits in any G-fag manifold Z = G/Q. The complex geometry of its open orbits D (flag domains) is studied from the point of view of compact complex submanifolds C (cycles) which arise as orbits of certain distinguished subgroups. Normal bundles E of the cycles are analyzed in some detail. It is shown that E is trivial if and only if D is holomorphically convex, in fact a product of C and a Hermitian symmetric space, and otherwise D is pseudoconcave.