Deformations of complex supermanifolds

Rothstein, Mitchell J.

doi:10.1090/S0002-9939-1985-0801334-0

Deformations of complex supermanifolds
HTML articles powered by AMS MathViewer

by Mitchell J. Rothstein PDF

Proc. Amer. Math. Soc. 95 (1985), 255-260 Request permission

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.

References

Marjorie Batchelor, The structure of supermanifolds, Trans. Amer. Math. Soc. 253 (1979), 329–338. MR 536951, DOI 10.1090/S0002-9947-1979-0536951-0
F. A. Berezin and D. A. Leĭtes, Supermanifolds, Dokl. Akad. Nauk SSSR 224 (1975), no. 3, 505–508 (Russian). MR 0402795
K. Gawędzki, Supersymmetries—mathematics of supergeometry, Ann. Inst. H. Poincaré Sect. A (N.S.) 27 (1977), no. 4, 335–366. MR 489701
Paul Green, On holomorphic graded manifolds, Proc. Amer. Math. Soc. 85 (1982), no. 4, 587–590. MR 660609, DOI 10.1090/S0002-9939-1982-0660609-6
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, DOI 10.2307/1970256
Bertram Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) Lecture Notes in Math., Vol. 570, Springer, Berlin, 1977, pp. 177–306. MR 0580292
D. A. Leĭtes, Introduction to the theory of supermanifolds, Uspekhi Mat. Nauk 35 (1980), no. 1(211), 3–57, 255 (Russian). MR 565567
I. B. Penkov, ${\cal D}$-modules on supermanifolds, Invent. Math. 71 (1983), no. 3, 501–512. MR 695902, DOI 10.1007/BF02095989
Abdus Salam and J. Strathdee, Superfields and Fermi-Bose symmetry, Phys. Rev. D (3) 11 (1975), 1521–1535. MR 408630, DOI 10.1103/PhysRevD.11.1521