RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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.

Full text: PDF file (8673 kB)
References: PDF file   HTML file

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
\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}


Linking options:
  • http://mi.mathnet.ru/eng/umn3728
  • http://mi.mathnet.ru/eng/umn/v31/i3/p129

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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:
    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
    2. I. F. Donin, “On deformations of non-compact complex spaces”, Russian Math. Surveys, 33:5 (1978), 181–182  mathnet  crossref  mathscinet  zmath
    3. A. S. Fainshtein, V. S. Shulman, “Fredholm complexes in Banach spaces”, Funct. Anal. Appl., 14:4 (1980), 322–323  mathnet  crossref  mathscinet  zmath  isi
    4. C. Bânicâ, M. Putinar, G. Schumacher, “Variation der globalen Ext in Deformationen kompakter komplexer Räume”, Math Ann, 250:3 (1980), 135  crossref  mathscinet  isi
    5. C. BĂnicĂ, M. Putinar, G. Schumacher, “Variation der globalen Ext in Deformationen kompakter komplexer Räume”, Math Ann, 250:2 (1980), 135  crossref
    6. Hubert Flenner, “Ein Kriterium für die Offenheit der Versalität”, Math Z, 178:4 (1981), 449  crossref  mathscinet  zmath  isi
    7. A. G. Aleksandrov, “Deformations of bouquets of quasihomogeneous one-dimensional singularities”, Funct. Anal. Appl., 15:1 (1981), 53–55  mathnet  crossref  mathscinet  zmath  isi
    8. Georg Schumacher, “Deformationen von Keimen eigentlicher, holomorpher Abbildungen”, manuscripta math, 39:1 (1982), 39  crossref  mathscinet  isi
    9. A. G. Aleksandrov, “Normal forms of one-dimensional quasihomogeneous complete intersections”, Math. USSR-Sb., 45:1 (1983), 1–30  mathnet  crossref  mathscinet  zmath
    10. V. P. Palamodov, “Deformations of Hopf manifolds and the Poincaré–Dulac theorem”, Funct. Anal. Appl., 17:4 (1983), 252–259  mathnet  crossref  mathscinet  zmath  isi
    11. A. Fialowski, “Deformations of Lie algebras”, Math. USSR-Sb., 55:2 (1986), 467–473  mathnet  crossref  mathscinet  zmath
    12. Jürgen Herzog, Rolf Waldi, “Cotangent functors of curve singularities”, manuscripta math, 55:3-4 (1986), 307  crossref  mathscinet  isi
    13. S Donaldson, R Friedman, Nonlinearity, 2:2 (1989), 197  crossref  mathscinet  zmath  adsnasa  isi
    14. T. Jong, D. Straten, “A deformation theory for non-isolated singularities”, Abh Math Semin Univ Hambg, 60:1 (1990), 177  crossref  mathscinet  zmath
    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
    17. Jan Stevens, “Computing Versal Deformations”, Experimental Mathematics, 4:2 (1995), 129  crossref
    18. Marco Manetti, “Iterated double covers and connected components of moduli spaces”, Topology, 36:3 (1997), 745  crossref
    19. Klaus Altmann, “Infinitesimal deformations and obstructions for toric singularities”, Journal of Pure and Applied Algebra, 119:3 (1997), 211  crossref
    20. Klaus Altmann, Arne B. Sletsjøe, “André–Quillen Cohomology of Monoid Algebras”, Journal of Algebra, 210:2 (1998), 708  crossref
    21. Alice Fialowski, Dmitry Fuchs, “Construction of Miniversal Deformations of Lie Algebras”, Journal of Functional Analysis, 161:1 (1999), 76  crossref
    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
    23. Yoshinori Namikawa, “On deformations of ℚ-factorial symplectic varieties”, crll, 2006:599 (2006), 97  crossref  mathscinet  zmath  isi  elib
    24. Victor P. Palamodov, “Infinitesimal Deformation Quantization of Complex Analytic Spaces”, Lett Math Phys, 79:2 (2007), 131  crossref  mathscinet  zmath  isi
    25. Yongnam Lee, Jongil Park, “A simply connected surface of general type with $p_g=0$ and $K^2=2$”, Invent math, 170:3 (2007), 483–505  crossref  mathscinet  zmath  isi
    26. Victor P. Palamodov, “Associative Deformations of Complex Analytic Spaces”, Lett Math Phys, 82:2-3 (2007), 191  crossref  mathscinet  zmath  isi
    27. Alice Fialowski, “Deformations in Mathematics and Physics”, Int J Theor Phys, 47:2 (2008), 333  crossref  mathscinet  zmath  isi
    28. Alice Fialowski, Ashis Mandal, Goutam Mukherjee, “Versal Deformations of Leibniz Algebras”, KAG, 2008, 1  crossref  mathscinet  isi
    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
    30. Ragnar-Olaf Buchweitz, Hubert Flenner, “Global Hochschild (co-)homology of singular spaces”, Advances in Mathematics, 217:1 (2008), 205  crossref
    31. Yongnam Lee, Jongil Park, “A construction of Horikawa surface via
      $${\mathbb{Q}}$$
      -Gorenstein smoothings”, Math Z, 2009  crossref
    32. Klaus Altmann, Jan Arthur Christophersen, “Deforming Stanley–Reisner schemes”, Math Ann, 2010  crossref
    33. Marco Manetti, “On some examples of obstructed irregular surfaces”, Sci. China Math, 2011  crossref
    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
    35. Reynir Axelsson, Indranil Biswas, Georg Schumacher, “Kähler structure on Hurwitz spaces”, manuscripta math, 2015  crossref
    36. Michele Rossi, “Deforming geometric transitions”, Int. J. Geom. Methods Mod. Phys, 2015, 1550059  crossref
    37. A. G. Aleksandrov, “Differential Forms on Zero-Dimensional Singularities”, Funct. Anal. Appl., 52:4 (2018), 241–257  mathnet  crossref  crossref  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:910
    Full text:376
    References:59
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019