Communications in Mathematics |

- 1 P.A. Solovyov Rybinsk State Aviation Technical University

Let $\mathbf L_k$ be the holomorphic line bundle of degree $k \in \mathbb Z$ on the projective line. Here, the tuples $(k_1 k_2 k_3 k_4)$ for which there does not exists homogeneous non-split supermanifolds $CP^{1|4}_{k_1 k_2 k_3 k_4}$ associated with the vector bundle $\mathbf L_{−k_1} \oplus \mathbf L _{−k_2} \oplus \mathbf L_{−k_3} \oplus \mathbf L_{−k_4}$ are classified. \\For many types of the remaining tuples, there are listed cocycles that determine homogeneous non-split supermanifolds. \\Proofs follow the lines indicated in the paper Bunegina V.A., Onishchik A.L., Homogeneous supermanifolds associated with the complex projective line.neous supermanifolds associated with the complex projective line. J. Math. Sci. V. 82 (1996)3503--3527.

Source: HAL:hal-03736767v2

Volume: Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik)

Published on: January 16, 2023

Accepted on: November 16, 2022

Submitted on: July 27, 2022

Keywords: Non-split homogeneous supermanifold,retract,holomorphic vector bundle,[MATH]Mathematics [math]

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