Homogeneous non-split superstrings of odd dimension 4

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