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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 6, Pages 1181–1199 (Mi izv1226)  

This article is cited in 6 scientific papers (total in 6 papers)

Affine curves of degree 6 and smoothings of a nondegenerate sixth order singular point

A. B. Korchagin, E. I. Shustin


Abstract: The paper is devoted to an isotopic classification of plane nonsingular real affine curves of degree 6 with maximum number of ovals (ten) and to the establishment of a connection between these curves and smoothings (nonsingular perturbations) of a nondegenerate sixth order singular point. Of 120 isotopic types admissible by known restrictions, 32 types are realized and 69 types are prohibited. It is proved that every smoothing of a nondegenerate sixth order singular point is the image of an affine curve of degree 6 under a homomorphism of the plane onto a neighborhood of the singular point.
Bibliography: 28 titles.

Full text: PDF file (2345 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:3, 501–520

Bibliographic databases:

UDC: 512.77
MSC: 14H20, 14H45
Received: 09.12.1986

Citation: A. B. Korchagin, E. I. Shustin, “Affine curves of degree 6 and smoothings of a nondegenerate sixth order singular point”, Izv. Akad. Nauk SSSR Ser. Mat., 52:6 (1988), 1181–1199; Math. USSR-Izv., 33:3 (1989), 501–520

Citation in format AMSBIB
\Bibitem{KorShu88}
\by A.~B.~Korchagin, E.~I.~Shustin
\paper Affine curves of degree~6 and smoothings of a~nondegenerate sixth order singular point
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 6
\pages 1181--1199
\mathnet{http://mi.mathnet.ru/izv1226}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=984215}
\zmath{https://zbmath.org/?q=an:0679.14011}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 3
\pages 501--520
\crossref{https://doi.org/10.1070/IM1989v033n03ABEH000854}


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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. E. I. Shustin, “New restrictions on the topology of real curves of degree a multiple of 8”, Math. USSR-Izv., 37:2 (1991), 421–443  mathnet  crossref  mathscinet  zmath  adsnasa
    2. S. Yu. Orevkov, “A new affine $M$-sextic. II”, Russian Math. Surveys, 53:5 (1998), 1099–1101  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. S. Yu. Orevkov, “A New Affine $M$-Sextic”, Funct. Anal. Appl., 32:2 (1998), 141–143  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. S. Yu. Orevkov, E. I. Shustin, “Pseudoholomorphic algebraically unrealizable curves”, Mosc. Math. J., 3:3 (2003), 1053–1083  mathnet  mathscinet  zmath
    5. S. Yu. Orevkov, “Arrangements of an $M$-quintic with respect to a conic that maximally intersects its odd branch”, St. Petersburg Math. J., 19:4 (2008), 625–674  mathnet  crossref  mathscinet  zmath  isi  elib
    6. S. Yu. Orevkov, E. I. Shustin, “Real algebraic and pseudoholomorphic curves on the quadratic cone and smoothings of singularity $X_{21}$”, St. Petersburg Math. J., 28:2 (2017), 225–257  mathnet  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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