We prove that any split DeWitt supermanifold is completely determined by a vector bundle over its body. In the real case, this implies the cohomological triviality of the structure sheaf. In the case of a complex split DeWitt supermanifold this permits one to compute the dimension of its Picard variety.
On DeWitt supermanifolds and their Picard variety
BARTOCCI, CLAUDIO;
1989-01-01
Abstract
We prove that any split DeWitt supermanifold is completely determined by a vector bundle over its body. In the real case, this implies the cohomological triviality of the structure sheaf. In the case of a complex split DeWitt supermanifold this permits one to compute the dimension of its Picard variety.
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