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By a result of Bochner and Montgomery the automorphism group of a compact complex manifold M carries the structure of a complex Lie group, whose Lie algebra is isomorphic to the Lie algebra of holomorphic vector fields on M. In this talk, the case of a compact complex supermanifold M is considered. In this setting, the Lie superalgebra Vec(M) of holomorphic super vector fields on M is finite-dimensional. We investigate how the automorphism group of a compact complex supermanifold M can be defined and prove that it carries the structure of a complex Lie supergroup with Lie superalgebra Vec(M). (This is joint work with Matthias Kalus.)

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Hannah Bergner, University of Freiburg
Seminarraum Theoretische Physik
Contact: Dominik Ostermayr