We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the geometry of superprojective spaces, we extend Donaldson’s definition of balanced manifolds to supermanifolds and we derive the new conditions of a balanced supermanifold. We apply the construction to superpoints viewed as submanifolds of superprojective spaces. We conclude with a list of open issues and interesting problems that can be addressed in the present context.
Balanced superprojective varieties / R. Catenacci, M. Debernardi, P. Grassi, D. Matessi. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 59:10(2009), pp. 1363-1378. [10.1016/j.geomphys.2009.07.002]
Balanced superprojective varieties
D. Matessi
2009
Abstract
We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the geometry of superprojective spaces, we extend Donaldson’s definition of balanced manifolds to supermanifolds and we derive the new conditions of a balanced supermanifold. We apply the construction to superpoints viewed as submanifolds of superprojective spaces. We conclude with a list of open issues and interesting problems that can be addressed in the present context.File | Dimensione | Formato | |
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