On holomorphic functions on a compact complex homogeneous supermanifold

Details On holomorphic functions on a compact complex homogeneous supermanifold On holomorphic functions on a compact complex homogeneous supermanifold

2010-07-09

arxiv.org/abs/1007.1576v1

Journal of Algebra 350 (2012) pp. 174-196

Mathematics

Differential Geometry

29 pages

Scientific paper

10.1016/j.jalgebra.2011.11.002

It is well-known that non-constant holomorphic functions do not exist on a compact complex manifold. This statement is false for a supermanifold with a compact reduction. In this paper we study the question under what conditions non-constant holomorphic functions do not exist on a compact homogeneous complex supermanifold. We describe also the vector bundles determined by split homogeneous complex supermanifolds. As an application, we compute the algebra of holomorphic functions on the classical flag supermanifolds which were introduced by Yu.I. Manin.

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