On complex-analytic $1|3$-dimensional supermanifolds associated with ${\mathbb{CP}}^1$

Abstract

We obtain a classification up to isomorphism of complex-analytic supermanifolds with underlying space ${\mathbb{CP}}^1$ of dimension $1|3$ with retract $(k,k,k)$, where $k\in \mathbb{Z}$. More precisely, we prove that classes of isomorphic complex-analytic supermanifolds of dimension $1|3$ with retract $(k,k,k)$ are in one-to-one correspondence with points of the following set: ${\mathbf{Gr}}_{4k-4,3}\cup {\mathbf{Gr}}_{4k-4,2}\cup {\mathbf{Gr}}_{4k-4,1}\cup {\mathbf{Gr}}_{4k-4,0}$ for $k\ge 2$. For $k<2$ all such supermanifolds are isomorphic to their retract $(k,k,k)$.

11p

Cited by in corpus (1)

• Complex supermanifolds of low odd dimension and the example of the complex projective line