A new generalization of Grassmannians in supergeometry, called $$\nu $$ -Grassmannians, are constructed by gluing $$\nu $$ -domains. By a $$\nu $$ -domain, we mean a superdomain with an odd involution say $$\nu $$ on its structure sheaf, as morphism of modules. Then we show that $$\nu $$ -Grassmannians are homogeneous superspaces. In addition, in the last section, a supergroup associated to the odd involution $$\nu $$ is introduced.

中文翻译：

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一类与奇数对合相关的齐次超空间

Grassmannians 在超几何中的一个新泛化，称为 $$\nu $$ -Grassmannians，是通过粘合 $$\nu $$ -域来构造的。通过 $$\nu $$ -域，我们指的是在其结构层上具有奇数对合的超域，例如 $$\nu $$，作为模块的态射。然后我们证明 $$\nu $$ -Grassmannians 是齐次超空间。此外，在最后一节中，介绍了与奇数对合 $$\nu $$ 相关联的超群。