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On holomorphic graded manifolds


Author: Paul Green
Journal: Proc. Amer. Math. Soc. 85 (1982), 587-590
MSC: Primary 32C10; Secondary 58A99
DOI: https://doi.org/10.1090/S0002-9939-1982-0660609-6
MathSciNet review: 660609
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Abstract: Kostant's definition of a $ {C^\infty }$-graded manifold is adapted to the holomorphic category. It is shown that, in contrast to the $ {C^\infty }$ case, there exist holomorphic graded manifolds with structure sheaf not isomorphic to the sheaf of sections of a bundle of exterior algebras.


References [Enhancements On Off] (What's this?)

  • [1] M. Batchelor, The structure of supermanifolds, Trans. Amer. Math. Soc. 253 (1979), 329-388. MR 536951 (80h:58002)
  • [2] B. Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential Geometrical Methods in Mathematical Physics, Lecture Notes in Math., vol. 570, Springer-Verlag, Berlin and New York, pp. 177-306. MR 0580292 (58:28326)

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DOI: https://doi.org/10.1090/S0002-9939-1982-0660609-6
Article copyright: © Copyright 1982 American Mathematical Society

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