2007/07/28 by R. Catenacci, M. Debernardi, Catenacci, R. +8
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0707.4246
24 pages, Latex, no figures
arxiv created 2007/07/28 · openalex publication_date 2007/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.