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Uspekhi Mat. Nauk, 1976, Volume 31, Issue 3(189), Pages 129–194 (Mi umn3728)  

This article is cited in 37 scientific papers (total in 37 papers)

Deformations of complex spaces

V. P. Palamodov

Abstract: This is a survey of the main directions in the theory of deformations of complex spaces. It touches on related questions: deformations of maps, cohomology of algebras, topology of singularities. The construction of the tangent complex and the tangent cohomology of a complex space is set out. The generalized Kodaira–Spencer class and the obstruction are defined as elements of the tangent cohomology; the latter is calculated in terms of the cohomology of the structure sheaf of the space. The constancy of the Euler characteristic of the tangent cohomology is established for deformations that realize versal and universal deformations of compact spaces and the connection of the geometry of a base of a versal deformation with the Massey operation in tangent cohomology is explained.

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English version:
Russian Mathematical Surveys, 1976, 31:3, 129–197

Bibliographic databases:

UDC: 519.9+513.83
MSC: 32G05, 32C35, 32C38, 58A30, 55S30
Received: 22.05.1975

Citation: V. P. Palamodov, “Deformations of complex spaces”, Uspekhi Mat. Nauk, 31:3(189) (1976), 129–194; Russian Math. Surveys, 31:3 (1976), 129–197

Citation in format AMSBIB
\by V.~P.~Palamodov
\paper Deformations of complex spaces
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 3(189)
\pages 129--194
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 3
\pages 129--197

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    This publication is cited in the following articles:
    1. V. S. Retakh, “Massey operations in Lie superalgebras and deformations of complexly analytic algebras”, Funct. Anal. Appl., 11:4 (1977), 319–321  mathnet  crossref  mathscinet  zmath
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    6. Hubert Flenner, “Ein Kriterium für die Offenheit der Versalität”, Math Z, 178:4 (1981), 449  crossref  mathscinet  zmath  isi
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    15. V. P. Palamodov, “Tangent fields on deformations of complex spaces”, Math. USSR-Sb., 71:1 (1992), 163–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. Ruud Pellikaan, “Deformations of hypersurfaces with a one-dimensional singular locus”, Journal of Pure and Applied Algebra, 67:1 (1990), 49  crossref
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    22. T. Hirsch, B. Martin, “Deformations with Section: Cotangent Cohomology, Flatness Conditions, and Modular Subgerms”, Journal of Mathematical Sciences (New York), 132:6 (2006), 739  crossref  mathscinet  zmath
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    29. Ragnar-Olaf Buchweitz, Hubert Flenner, “The global decomposition theorem for Hochschild (co-)homology of singular spaces via the Atiyah–Chern character”, Advances in Mathematics, 217:1 (2008), 243  crossref
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    34. B. G. Konopelchenko, G. Ortenzi, “Cohomological and Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of the Sato Grassmannian”, Theoret. and Math. Phys., 177:2 (2013), 1479–1491  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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