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Uspekhi Mat. Nauk, 2007, Volume 62, Issue 6(378), Pages 3–86 (Mi umn8530)  

This article is cited in 11 scientific papers (total in 11 papers)

Hurwitz curves

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The present paper is a survey of recent results about Hurwitz curves, their braid monodromy invariants, and their applications to $H$-isotopy and regular homotopy problems. The second part of the survey is devoted to a discussion of the applicability of braid monodromy invariants of branch curves for generic coverings of the projective plane as invariants distinguishing connected components of the moduli space of algebraic surfaces (in the algebraic case) and distinguishing symplectic structures on four-dimensional varieties (in the symplectic case).

DOI: https://doi.org/10.4213/rm8530

Full text: PDF file (1222 kB)
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English version:
Russian Mathematical Surveys, 2007, 62:6, 1043–1119

Bibliographic databases:

Document Type: Article
UDC: 514.7
MSC: Primary 14E20; Secondary 14H30, 14H55
Received: 16.01.2007

Citation: Vik. S. Kulikov, “Hurwitz curves”, Uspekhi Mat. Nauk, 62:6(378) (2007), 3–86; Russian Math. Surveys, 62:6 (2007), 1043–1119

Citation in format AMSBIB
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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. Vik. S. Kulikov, “Factorization semigroups and irreducible components of the Hurwitz space”, Izv. Math., 75:4 (2011), 711–748  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Degtyarev A., “Hurwitz equivalence of braid monodromies and extremal elliptic surfaces”, Proc. Lond. Math. Soc. (3), 103:6 (2011), 1083–1120  crossref  mathscinet  zmath  isi  scopus
    3. Degtyarev A., “The fundamental group of a generalized trigonal curve”, Osaka J. Math., 48:3 (2011), 749–782  mathscinet  zmath  isi
    4. Ciliberto C., Flamini F., “On the branch curve of a general projection of a surface to a plane”, Trans. Amer. Math. Soc., 363:7 (2011), 3457–3471  crossref  mathscinet  zmath  isi  elib  scopus
    5. Degtyarev A., “Topology of plane algebraic curves: the algebraic approach”, Topology of algebraic varieties and singularities, Contemp. Math., 538, Amer. Math. Soc., Providence, RI, 2011, 137–161  crossref  mathscinet  zmath  isi
    6. Vik. S. Kulikov, “Factorizations in finite groups”, Sb. Math., 204:2 (2013), 237–263  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Vik. S. Kulikov, V. M. Kharlamov, “Covering semigroups”, Izv. Math., 77:3 (2013), 594–626  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. F.A.. Bogomolov, V.S.. Kulikov, “The ambiguity index of an equipped finite group”, European Journal of Mathematics, 2015  crossref  mathscinet  scopus
    9. Vik. S. Kulikov, “Dualizing coverings of the plane”, Izv. Math., 79:5 (2015), 1013–1042  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    10. Vik. S. Kulikov, “Plane rational quartics and K3 surfaces”, Proc. Steklov Inst. Math., 294 (2016), 95–128  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    11. Vik. S. Kulikov, E. I. Shustin, “On $G$-Rigid Surfaces”, Proc. Steklov Inst. Math., 298 (2017), 133–151  mathnet  crossref  crossref  isi  elib
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