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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Complex orbits of solvable groups


Author: Dennis M. Snow
Journal: Proc. Amer. Math. Soc. 110 (1990), 689-696
MSC: Primary 32M10; Secondary 14L30
DOI: https://doi.org/10.1090/S0002-9939-1990-1028050-9
MathSciNet review: 1028050
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Abstract: The following structure theorems are proved: An orbit of a real solvable Lie group in projective space that is a complex submanifold is isomorphic to $ {{\mathbf{C}}^k} \times {({{\mathbf{C}}^ * })^m} \times \Omega $, where $ \Omega $ is an open orbit of a real solvable Lie group in a projective rational variety. Also, any homogeneous space of a complex Lie group that is isomorphic to $ {{\mathbf{C}}^n}$ can be realized as an orbit in some projective space. As a consequence, left-invariant complex structures on real solvable Lie groups are always induced from complex orbits in projective space.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1028050-9
Article copyright: © Copyright 1990 American Mathematical Society