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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 5, Pages 1026–1058 (Mi izv2190)  

This article is cited in 28 scientific papers (total in 28 papers)

Locally semiuniversal flat deformations of isolated singularities of complex spaces

G. N. Tyurina

Abstract: In this study we construct the minimal locally semiuniversal deformation of a normal isolated singularity $x_0\in X_0$ for which $\operatorname{Ext}^2_{0(x_0)}(\Omega(X_0), 0(X_0))_{x_0}=0$, where $\Omega(X_0)$ is the sheaf of germs of one-dimensional holomorphic forms in the complex space $(X_0,0(X_0))$.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 33:5, 967–999

Bibliographic databases:

UDC: 519.4
MSC: 32S30, 32A19, 32B10, 32G05
Received: 26.11.1968

Citation: G. N. Tyurina, “Locally semiuniversal flat deformations of isolated singularities of complex spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 33:5 (1969), 1026–1058; Math. USSR-Izv., 33:5 (1969), 967–999

Citation in format AMSBIB
\by G.~N.~Tyurina
\paper Locally semiuniversal flat deformations of isolated singularities of complex spaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 5
\pages 1026--1058
\jour Math. USSR-Izv.
\yr 1969
\vol 33
\issue 5
\pages 967--999

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    This publication is cited in the following articles:
    1. G. N. Tyurina, “Resolution of singularities of plane deformations of double rational points”, Funct. Anal. Appl., 4:1 (1970), 68–73  mathnet  crossref  mathscinet  zmath
    2. V. I. Arnol'd, “Lectures on bifurcations in versal families”, Russian Math. Surveys, 27:5 (1972), 54–123  mathnet  crossref  mathscinet  zmath
    3. I. F. Donin, “Complete families of deformations of germs of complex spaces”, Math. USSR-Sb., 18:3 (1972), 397–406  mathnet  crossref  mathscinet  zmath
    4. S. G. Tankeev, “On a global theory of moduli of algebraic surfaces of general type”, Math. USSR-Izv., 6:6 (1972), 1200–1216  mathnet  crossref  mathscinet  zmath
    5. V. I. Arnol'd, “Normal forms for functions near degenerate critical points, the Weyl groups of $A_k$, $D_k$, $E_k$ and Lagrangian singularities”, Funct. Anal. Appl., 6:4 (1972), 254–272  mathnet  crossref  mathscinet  zmath
    6. V. I. Arnol'd, “Remarks on the stationary phase method and Coxeter numders”, Russian Math. Surveys, 28:5 (1973), 19–48  mathnet  crossref  mathscinet  zmath
    7. H.C Pinkham, “Deformations of cones with negative grading”, Journal of Algebra, 30:1-3 (1974), 92  crossref
    8. V. I. Arnol'd, “Critical points of smooth functions and their normal forms”, Russian Math. Surveys, 30:5 (1975), 1–75  mathnet  crossref  mathscinet  zmath
    9. Günther Trautmann, “Deformationen von isolierten Singularitäten kohärenter analytischer Garben”, Math Ann, 223:1 (1976), 71  crossref  mathscinet
    10. Gert-Martin Greuel, Lê Dũng Tráng, “Spitzen, Doppelpunkte und vertikale Tangenten in der Diskriminante verseller Deformationen von vollständigen Durchschnitten”, Math Ann, 222:1 (1976), 71  crossref  mathscinet  zmath
    11. V. P. Palamodov, “Deformations of complex spaces”, Russian Math. Surveys, 31:3 (1976), 129–197  mathnet  crossref  mathscinet  zmath
    12. Joël Briançon, “Description de Hilb n C{x, y}”, Invent math, 41:1 (1977), 45  crossref  mathscinet  zmath  adsnasa
    13. R. Mandelbaum, M. Schaps, “On the smoothing and deformation of perfect varieties”, Math Ann, 226:1 (1977), 67  crossref  mathscinet  zmath
    14. Gert -Martin Greuel, “Die Zahl der Spitzen und die Jacobi-Algebra einer isolierten Hyperflächensingularität”, manuscripta math, 21:3 (1977), 227  crossref  mathscinet  zmath
    15. S. M. Gusein-Zade, “The monodromy groups of isolated singularities of hypersurfaces”, Russian Math. Surveys, 32:2 (1977), 23–69  mathnet  crossref  mathscinet  zmath
    16. Alan H. Durfee, “The signature of smoothings of complex surface singularities”, Math Ann, 232:1 (1978), 85  crossref  mathscinet  zmath
    17. Martin Golubitsky, “An Introduction to Catastrophe Theory and Its Applications”, SIAM Rev, 20:2 (1978), 352  crossref  mathscinet  zmath
    18. Gert-Martin Greuel, “Dualität in der lokalen Kohomologie isolierter Singularitäten”, Math Ann, 250:3 (1980), 157  crossref  crossref  mathscinet  zmath  isi
    19. R. D. Stafford, “Infinitesimally complete deformations over nonsingular bases”, Abh Math Semin Univ Hambg, 51:1 (1981), 196  crossref  mathscinet  zmath
    20. A. G. Aleksandrov, “Normal forms of one-dimensional quasihomogeneous complete intersections”, Math. USSR-Sb., 45:1 (1983), 1–30  mathnet  crossref  mathscinet  zmath
    21. J. -M. Bismut, J. -B. Bost, “Fibrés déterminants, métriques de Quillen et dégénérescence des courbes”, Acta Math, 165:1 (1990), 1  crossref  mathscinet  zmath  isi
    22. Theo de Jong, “The virtual number of D∞ points I”, Topology, 29:2 (1990), 175  crossref
    23. J. Stevens, “On the computation of versal deformations”, Journal of Mathematical Sciences (New York), 82:5 (1996), 3713  crossref  mathscinet  zmath
    24. Victor P. Palamodov, “Infinitesimal Deformation Quantization of Complex Analytic Spaces”, Lett Math Phys, 79:2 (2007), 131  crossref  mathscinet  zmath  isi
    25. M. E. Hernandes, M. E. Rodrigues Hernandes, M. A. S. Ruas, “
      -codimension of germs of analytic curves”, manuscripta math, 124:2 (2007), 237  crossref  mathscinet  zmath  isi
    26. W. Domitrz, S. Janeczko, M. Zhitomirskii, “Symplectic singularities of varieties: The method of algebraic restrictions”, crll, 2008:618 (2008), 197  crossref  mathscinet  zmath  isi  elib
    27. Mauricio Garay, “An abstract KAM theorem”, Mosc. Math. J., 14:4 (2014), 745–772  mathnet  crossref  mathscinet
    28. S. O. Gorchinskiy, D. N. Tyurin, “Relative Milnor $K$-groups and differential forms of split nilpotent extensions”, Izv. Math., 82:5 (2018), 880–913  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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