Geodesic
Homogeneous and $\overline0$-homogeneous supermanifolds with retract $\mathbb{CP}^{1|4}_{kk20}$ when $k\ge 2$
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 3, pp. 14-21

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This paper contain the description of non-split even-homogeneous supermanifolds over the complex projective line whose retract corresponds to a holomorphic vector bundle of the signature $(k,k,2,0),$ where $k\ge 2$. We prove that there are no non-split homogeneous supermanifolds in this case. See [3] and [4] for more information about the complex supermanifolds theory.
Keywords: complex supermanifold, homogeneous complex supermanifold, tangent sheaf.
Mots-clés : retract 
@article{MAIS_2009_16_3_a1,
     author = {M. A. Bashkin},
     title = {Homogeneous and $\overline0$-homogeneous supermanifolds with retract $\mathbb{CP}^{1|4}_{kk20}$ when $k\ge 2$},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {14--21},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2009_16_3_a1/}
}
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M. A. Bashkin. Homogeneous and $\overline0$-homogeneous supermanifolds with retract $\mathbb{CP}^{1|4}_{kk20}$ when $k\ge 2$. Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 3, pp. 14-21. http://geodesic.mathdoc.fr/item/MAIS_2009_16_3_a1/