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Mat. Sb., 1998, Volume 189, Number 2, Pages 111–136 (Mi msb295)  

This article is cited in 4 scientific papers (total in 5 papers)

Homogeneous supermanifolds associated with complex projective space. I

A. L. Onishchik, O. V. Platonova

Yaroslavl State Technical University

Abstract: Homogeneous and evenly homogeneous complex supermanifolds of dimension $n|m$ with reduction equal to the complex projective space $\mathbb {CP}^n$ are studied. Under the assumption that $m\leqslant n$, all split supermanifolds of this type are classified and their 1-cohomology with values in the tangent sheaf (which is invariant under the projective group) is calculated.

DOI: https://doi.org/10.4213/sm295

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English version:
Sbornik: Mathematics, 1998, 189:2, 265–289

Bibliographic databases:

UDC: 515.177
MSC: 32C11, 32M10
Received: 03.03.1997

Citation: A. L. Onishchik, O. V. Platonova, “Homogeneous supermanifolds associated with complex projective space. I”, Mat. Sb., 189:2 (1998), 111–136; Sb. Math., 189:2 (1998), 265–289

Citation in format AMSBIB
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\by A.~L.~Onishchik, O.~V.~Platonova
\paper Homogeneous supermanifolds associated with complex projective space.~I
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 2
\pages 111--136
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\jour Sb. Math.
\yr 1998
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\issue 2
\pages 265--289
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    This publication is cited in the following articles:
    1. A. L. Onishchik, O. V. Platonova, “Homogeneous supermanifolds associated with complex projective space. II”, Sb. Math., 189:3 (1998), 421–441  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, V. G. Durnev, R. Zulanke, L. S. Kazarin, D. A. Leites, V. V. Serganova, V. M. Tikhomirov, “Arkadii L'vovich Onishchik (on his 70th birthday)”, Russian Math. Surveys, 58:6 (2003), 1245–1253  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. N. I. Ivanova, A. L. Onishchik, “Parabolic Subalgebras and Gradings of Reductive Lie Superalgebras”, Journal of Mathematical Sciences, 152:1 (2008), 1–60  mathnet  crossref  mathscinet  zmath  elib
    4. Onishchik, AL, “Homogeneous supermanifolds over Grassmannians”, Journal of Algebra, 313:1 (2007), 320  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Vishnyakova E.G., “Even-Homogeneous Supermanifolds on the Complex Projective Line”, Differ. Geom. Appl., 31:5 (2013), 698–706  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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