On complex-analytic 1|3-dimensional supermanifolds associated with \mathbbCP¹

2013/11/28 by Elizaveta Vishnyakova, E. G. Vishnyakova, Vishnyakova, E. G.
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG

paper · pdf · doi:10.48550/arxiv.1311.7291

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arxiv created 2013/11/28 · arxiv updated 2013/12/02

Abstract

We obtain a classification up to isomorphism of complex-analytic supermanifolds with underlying space \mathbbCP¹ of dimension 1|3 with retract (k,k,k), where k∈ 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: Gr_4k-4,3 ∪ Gr_4k-4,2 ∪ Gr_4k-4,1 ∪ Gr_4k-4,0 for k ≥ 2. For k < 2 all such supermanifolds are isomorphic to their retract (k,k,k).

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