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

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

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
\Bibitem{Pal76} \by V.~P.~Palamodov \paper Deformations of complex spaces \jour Uspekhi Mat. Nauk \yr 1976 \vol 31 \issue 3(189) \pages 129--194 \mathnet{http://mi.mathnet.ru/umn3728} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=508121} \zmath{https://zbmath.org/?q=an:0332.32013|0347.32009} \transl \jour Russian Math. Surveys \yr 1976 \vol 31 \issue 3 \pages 129--197 \crossref{https://doi.org/10.1070/RM1976v031n03ABEH001549} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
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