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Mat. Sb., 1998, Volume 189, Number 9, Pages 23–60 (Mi msb349)  

This article is cited in 10 scientific papers (total in 10 papers)

Deformations of non-compact complex curves and envelopes of meromorphy of spheres

S. M. Ivashkovicha, V. V. Shevchishinb

a University of Sciences and Technologies
b Ruhr-Universität Bochum

Abstract: The paper discusses the properties of the envelopes of meromorphy of neighbourhoods of symplectically immersed two-spheres in complex Kahler surfaces. The method used to study the envelopes of meromorphy is based on Gromov's theory of pseudoholomorphic curves. The exposition includes a construction of a complete family of holomorphic deformations of a non-compact complex curve in a complex manifold parametrized by a finite-codimensional analytic subset of a Banach ball. The existence of this family is used to prove a generalization of Levi's continuity principle, which is applied to describe envelopes of meromorphy.

DOI: https://doi.org/10.4213/sm349

Full text: PDF file (584 kB)
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English version:
Sbornik: Mathematics, 1998, 189:9, 1295–1333

Bibliographic databases:

UDC: 517.55+515.17
MSC: Primary 32D10, 58F05; Secondary 32A20, 53C15
Received: 23.01.1998

Citation: S. M. Ivashkovich, V. V. Shevchishin, “Deformations of non-compact complex curves and envelopes of meromorphy of spheres”, Mat. Sb., 189:9 (1998), 23–60; Sb. Math., 189:9 (1998), 1295–1333

Citation in format AMSBIB
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\paper Deformations of non-compact complex curves and envelopes of meromorphy of spheres
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 9
\pages 23--60
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\transl
\jour Sb. Math.
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\vol 189
\issue 9
\pages 1295--1333
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Yu. Nemirovski, “Complex analysis and differential topology on complex surfaces”, Russian Math. Surveys, 54:4 (1999), 729–752  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Vik. S. Kulikov, D. Auroux, V. V. Shevchishin, “Regular homotopy of Hurwitz curves”, Izv. Math., 68:3 (2004), 521–542  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Barrett, DE, “The role of Fourier modes in extension theorems of Hartogs-Chirka type”, Mathematische Zeitschrift, 249:4 (2005), 883  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Itenberg, I, “Logarithmic asymptotics of the genus zero Gromov-Witten invariants of the blown up plane”, Geometry & Topology, 9 (2005), 483  crossref  mathscinet  zmath  isi
    5. Forstneric, F, “Manifolds of holomorphic mappings from strongly pseudoconvex domains”, Asian Journal of Mathematics, 11:1 (2007), 113  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Drinovec-Drnovsek, B, “Approximation of holomorphic mappings on strongly pseudoconvex domains”, Forum Mathematicum, 20:5 (2008), 817  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Burglind Jöricke, “Envelopes of holomorphy and holomorphic discs”, Invent math, 2009  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Vsevolod V. Shevchishin, “A moduli space of non-compact curves on a complex surface”, Complex Variables and Elliptic Equations, 2011, 1  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Ivashkovich S., “Vanishing Cycles in Holomorphic Foliations by Curves and Foliated Shells”, Geom Funct Anal, 21:1 (2011), 70–140  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    10. Ionel E.-N., Parker T.H., “The Gopakumar-Vafa Formula For Symplectic Manifolds”, Ann. Math., 187:1 (2018), 1–64  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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