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Abstract: We first review the definition of superprojective spaces from thefunctor-of-points perspective. We derive the relation between superprojectivespaces and supercosets in the framework of the theory of sheaves. As anapplication of the geometry of superprojective spaces, we extend Donaldson-sdefinition of balanced manifolds to supermanifolds and we derive the newconditions of a balanced supermanifold. We apply the construction tosuperpoints viewed as submanifolds of superprojective spaces. We conclude witha list of open issues and interesting problems that can be addressed in thepresent context.

Author: R. Catenacci, M. Debernardi, P.A. Grassi, D. Matessi


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