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Article Dans Une Revue Communications in Mathematics Année : 2023

Homogeneous non-split superstrings of odd dimension 4

Résumé

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.
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Dates et versions

hal-03736767 , version 1 (22-07-2022)
hal-03736767 , version 2 (04-01-2023)

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Mikhail Bashkin. Homogeneous non-split superstrings of odd dimension 4. Communications in Mathematics, In press, Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik), ⟨10.46298/cm.9843⟩. ⟨hal-03736767v2⟩
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