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New M-Curve of Degree 8

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Functional Analysis and Its Applications Aims and scope

Abstract

We construct a plane real algebraic curve of degree 8 with 22 ovals (an M-curve) realizing the isotopy type \(\left\langle {7 \sqcup 1\left\langle {2 \sqcup 1\left\langle {11} \right\rangle } \right\rangle } \right\rangle\) whose realizability was unknown.

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References

  1. B. Chevallier, Funkts. Anal. Prilozhen., 36, No.1, 90–93 (2002); English transl. Funct. Anal. Appl., 36, No. 1, 76–78 (2002)

    Google Scholar 

  2. A. B. Korchagin, The first part of Hilbert's sixteenth problem: history and main results, Math. Series, Texas Tech University, Vol. 19, 1997, pp. 85–140.

    Google Scholar 

  3. S. Yu. Orevkov, “Classification of flexible M-curves of degree 8 up to isotopy,” GAFA, Geom. Funct. Anal. (to appear).

  4. E. I. Shustin, Algebra Analiz, 11, No.5, 221–249 (1999); English transl. St. Petersburg Math. J., 11, 883–908 (2000).

    Google Scholar 

  5. O. Ya. Viro, Real algebraic varieties with prescribed topological properties, D. Sc. Thesis [in Russian], Leningrad State University; English transl. Chapter 1, Patchworking real algebraic varieties, http://www.math.uu.se/~oleg.

  6. O. Ya. Viro, Algebra Analiz, 1, No.5, 1–73 (1990); English transl. Leningrad Math. J., 1, 1059–1134 (1990).

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Orevkov, S.Y. New M-Curve of Degree 8. Functional Analysis and Its Applications 36, 247–249 (2002). https://doi.org/10.1023/A:1020118609560

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  • DOI: https://doi.org/10.1023/A:1020118609560

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