Deformations of complex supermanifolds
Author:
Mitchell J. Rothstein
Journal:
Proc. Amer. Math. Soc. 95 (1985), 255-260
MSC:
Primary 32G05; Secondary 58A50
DOI:
https://doi.org/10.1090/S0002-9939-1985-0801334-0
MathSciNet review:
801334
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Abstract | References | Similar Articles | Additional Information
Abstract: The supermanifold analogue of the Kodaira-Nirenberg-Spencer existence theorem for deformations of complex structures is given. It is shown that every complex supermanifold is a deformation of a vector bundle.
- [1] Marjorie Batchelor, The structure of supermanifolds, Trans. Amer. Math. Soc. 253 (1979), 329–338. MR 536951, https://doi.org/10.1090/S0002-9947-1979-0536951-0
- [2] F. A. Berezin and D. A. Leĭtes, Supermanifolds, Dokl. Akad. Nauk SSSR 224 (1975), no. 3, 505–508 (Russian). MR 0402795
- [3] K. Gawędzki, Supersymmetries—mathematics of supergeometry, Ann. Inst. H. Poincaré Sect. A (N.S.) 27 (1977), no. 4, 335–366. MR 489701
- [4] Paul Green, On holomorphic graded manifolds, Proc. Amer. Math. Soc. 85 (1982), no. 4, 587–590. MR 660609, https://doi.org/10.1090/S0002-9939-1982-0660609-6
- [5] K. Kodaira, L. Nirenberg, and D. C. Spencer, On the existence of deformations of complex analytic structures, Ann. of Math. (2) 68 (1958), 450–459. MR 112157, https://doi.org/10.2307/1970256
- [6] Bertram Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) Springer, Berlin, 1977, pp. 177–306. Lecture Notes in Math., Vol. 570. MR 0580292
- [7] D. A. Leĭtes, Introduction to the theory of supermanifolds, Uspekhi Mat. Nauk 35 (1980), no. 1(211), 3–57, 255 (Russian). MR 565567
- [8] I. B. Penkov, \cal𝐷-modules on supermanifolds, Invent. Math. 71 (1983), no. 3, 501–512. MR 695902, https://doi.org/10.1007/BF02095989
- [9] Abdus Salam and J. Strathdee, Superfields and Fermi-Bose symmetry, Phys. Rev. D (3) 11 (1975), 1521–1535. MR 408630, https://doi.org/10.1103/PhysRevD.11.1521
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1985-0801334-0
Article copyright:
© Copyright 1985
American Mathematical Society