Geodesic
Homogeneous supermanifolds associated with complex projective space. II
Sbornik. Mathematics, Tome 189 (1998) no. 3, pp. 421-441 
A. L. Onishchik; O. V. Platonova. Homogeneous supermanifolds associated with complex projective space. II. Sbornik. Mathematics, Tome 189 (1998) no. 3, pp. 421-441. http://geodesic.mathdoc.fr/item/SM_1998_189_3_a4/
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     title = {Homogeneous supermanifolds associated with complex projective space. {II}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The study of homogeneous and evenly homogeneous complex supermanifolds of dimension $n|m$ whose reduction is the complex projective space $\mathbb {CP}^n$ is continued. All non-split supermanifolds of this type with retract admitting the full projective group as group of automorphisms are classified. The cohomology with values in the tangent sheaf is calculated for homogeneous supermanifolds satisfying the above-mentioned conditions.

[1] Onischik A. L., Platonova O. V., “Odnorodnye supermnogoobraziya, svyazannye s kompleksnym proektivnym prostranstvom, I”, Matem. sb., 189:2 (1998), 111–136 | MR | Zbl

[2] Platonova O. V., “Ob odnorodnykh supermnogoobraziyakh razmernosti $2\mid 2$”, UMN, 50:6 (1995), 205–206 | MR | Zbl

[3] Platonova O. V., “Ob odnorodnykh supermnogoobraziyakh, svyazannykh s kompleksnym proektivnym prostranstvom”, Akt. problemy estestv. nauk. Matematika. Informatika, Yaroslavl, 1995, 46–47

[4] Green P., “On holomorphic graded manifolds”, Proc. Amer. Math. Soc., 85 (1982), 587–590 | DOI | MR | Zbl

[5] Rothstein M. J., “Deformations of complex supermanifolds”, Proc. Amer. Math. Soc., 95 (1985), 255–260 | DOI | MR | Zbl

[6] Onishchik A. L., Non-split supermanifolds associated with the cotangent bundle, Preprint No 109, Université de Poitiers, Département de Math., 1997 | MR | Zbl

[7] Manin Yu. I., Kalibrovochnye polya i kompleksnaya geometriya, Nauka, M., 1984 | MR

[8] Bunegina V. A., Onishchik A. L., “Homogeneous supermanifolds associated with the complex projective line”, J. Math. Sci., 82 (1996), 3503–3527 | DOI | MR | Zbl

[9] Onishchik A. L., “A spectral sequence for the tangent sheaf cohomology of a supermanifold”, Sophus Lie '94, Proceedings of Conference ISLC (Moscow, August 1994), Kluwer Acad. Publ., Dordrecht, 1997, 23–38

[10] Onishchik A. L., About derivations and vector-valued differential forms, No 181, Inst. Math. Ruhr-Universität Bochum, 1995

[11] Vaintrob A. Yu., “Deformatsii kompleksnykh superprostranstv i kogerentnykh puchkov na nikh”, Itogi nauki i tekhniki. Sovr. probl. matem. Noveishie dostizheniya, 32, VINITI, M., 1988, 27–70