Homogeneous and 0-homogeneous supermanifolds with retract CP(1|4 kk20) when k >= 2

Abstract

This paper contain the description of non-split even-homogeneous supermanifolds over the complex projective line whose retract corresponds to a holomorphic vector bundle of the signature (k,k, 2,0), where k >= 2. We prove that there are no non-split homogeneous supermanifolds in this case. See [3] and [4] for more information about the complex supermanifolds theory.

Keywords

• complex supermanifold
• homogeneous complex supermanifold
• retract
• tangent sheaf