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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 3, Pages 540–591 (Mi izv2380)  

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

Asymptotic Hodge structure in the vanishing cohomology

A. N. Varchenko


Abstract: The asymptotics of integrals which depend on a critical point of a holomorphic function and the mixed Hodge structure in the vanishing cohomology are compared.
Bibliography: 37 titles.

Full text: PDF file (5372 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1982, 18:3, 469–512

Bibliographic databases:

UDC: 513.836
MSC: Primary 14B05; Secondary 32B30, 32C36, 32G20, 32J25, 14C30
Received: 24.03.1980

Citation: A. N. Varchenko, “Asymptotic Hodge structure in the vanishing cohomology”, Izv. Akad. Nauk SSSR Ser. Mat., 45:3 (1981), 540–591; Math. USSR-Izv., 18:3 (1982), 469–512

Citation in format AMSBIB
\Bibitem{Var81}
\by A.~N.~Varchenko
\paper Asymptotic Hodge structure in the vanishing cohomology
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 3
\pages 540--591
\mathnet{http://mi.mathnet.ru/izv2380}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=623350}
\zmath{https://zbmath.org/?q=an:0489.14003|0476.14002}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 3
\pages 469--512
\crossref{https://doi.org/10.1070/IM1982v018n03ABEH001395}


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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:
    1. A. N. Varchenko, “The complex exponent of a singularity does not change along strata $\mu=\mathrm{const}$”, Funct. Anal. Appl., 16:1 (1982), 1–9  mathnet  crossref  mathscinet  zmath  isi
    2. A. N. Varchenko, A. B. Givental', “Mapping of periods and intersection form”, Funct. Anal. Appl., 16:2 (1982), 83–93  mathnet  crossref  mathscinet  zmath  isi
    3. V. I. Arnol'd, “Singularities of systems of rays”, Russian Math. Surveys, 38:2 (1983), 87–176  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. N. Varchenko, “Semicontinuity of the complex singularity index”, Funct. Anal. Appl., 17:4 (1983), 307–309  mathnet  crossref  mathscinet  zmath  isi
    5. A. N. Varchenko, S. V. Chmutov, “Finite irreducible groups, generated by reflections, are monodromy groups of suitable singularities”, Funct. Anal. Appl., 18:3 (1984), 171–183  mathnet  crossref  mathscinet  zmath  isi
    6. J. Scherk, J. H. M. Steenbrink, “On the mixed Hodge structure on the cohomology of the Milnor fibre”, Math Ann, 271:4 (1985), 641  crossref  mathscinet  zmath  isi
    7. J. H. M. Steenbrink, “Semicontinuity of the singularity spectrum”, Invent math, 79:3 (1985), 557  crossref  mathscinet  zmath  adsnasa  isi
    8. Duco Straten, Joseph Steenbrink, “Extendability of holomorphic differential forms near isolated hypersurface singularities”, Abh Math Semin Univ Hambg, 55:1 (1985), 97  crossref  mathscinet
    9. A. N. Varchenko, “On the local residue and the intersection form on the vanishing cohomology”, Math. USSR-Izv., 26:1 (1986), 31–52  mathnet  crossref  mathscinet  zmath
    10. A. N. Varchenko, “Local classification of volume forms in the presence of a hypersurface”, Funct. Anal. Appl., 19:4 (1985), 269–276  mathnet  crossref  mathscinet  zmath  isi
    11. V. Navarro Aznar, “Sur la théorie de Hodge-Deligne”, Invent math, 90:1 (1987), 11  crossref  mathscinet  zmath  isi
    12. A. N. Varchenko, “On normal forms of nonsmoothness of solutions of hyperbolic equations”, Math. USSR-Izv., 30:3 (1988), 615–628  mathnet  crossref  mathscinet  zmath
    13. A. N. Varchenko, “The period map and the discriminant”, Math. USSR-Sb., 62:1 (1989), 65–81  mathnet  crossref  mathscinet  zmath
    14. B. Lichtin, “Poles of |f(z,w)|2s and roots of theB-function”, Ark Mat, 27:1-2 (1989), 283  crossref  mathscinet  zmath  isi
    15. M. G. M. Doorn, J. H. M. Steenbrink, “A supplement to the monodromy theorem”, Abh Math Semin Univ Hambg, 59:1 (1989), 225  crossref  mathscinet  zmath
    16. Yakov Karpishpan, “Torelli theorems for singularities”, Invent math, 100:1 (1990), 97  crossref  mathscinet  zmath  isi
    17. Ben Lichtin, “Periods and the asymptotics of a diophantine problem: I”, Ark Mat, 30:1-2 (1992), 105  crossref  mathscinet  zmath  isi
    18. A. Libgober, “Position of singularities of hypersurfaces and the topology of their complements”, Journal of Mathematical Sciences (New York), 82:1 (1996), 3194  crossref  mathscinet  zmath
    19. C SABBAH, “Hypergeometric period for a tame polynomial”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 328:7 (1999), 603  crossref
    20. A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. F.J. Castro-Jiménez, J.M. Ucha-Enríquez, “Explicit Comparison Theorems for D -modules”, Journal of Symbolic Computation, 32:6 (2001), 677  crossref
    22. Proc. Steklov Inst. Math., 238 (2002), 88–96  mathnet  mathscinet  zmath
    23. A. L. KHOLODENKO, “NEW STRING AMPLITUDES FROM OLD FERMAT (HYPER)SURFACES”, Int. J. Mod. Phys. A, 19:11 (2004), 1655  crossref
    24. Carlos Galindo, Francisco Monserrat, “The Poincaré series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface”, Advances in Mathematics, 225:2 (2010), 1046  crossref
    25. A. Melle-Hernández, T. Torrelli, Willem Veys, “Monodromy Jordan blocks, b-functions and poles of zeta functions for germs of plane curves”, Journal of Algebra, 324:6 (2010), 1364  crossref
    26. Mustata M., “Impanga Lecture Notes on Log Canonical Thresholds”, Contribution to Algebraic Geometry: Impanga Lecture Note, EMS Ser. Congr. Rep., ed. Pragacz P., Eur. Math. Soc., 2012, 407–442  mathscinet  isi
    27. S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Russian Math. Surveys, 72:1 (2017), 1–32  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    28. Sabbah C., “Some Properties and Applications of Brieskorn Lattices”, J. Singul., 18 (2018), 238–247  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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