A Novel Supergeometric Generalization of Grassmannians

Abstract

A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a \nu\- domain, i.e. a superdomain with an odd involution, say \nu\, on their structure sheaf considered as a sheaf of C^\infty_{R^m}-modules.