New $M$-Curve of Degree 8
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 90-93
Cet article a éte moissonné depuis la source Math-Net.Ru
We construct a plane real algebraic curve of degree $8$ with $22$ ovals (an $M$-curve) realizing the isotopy type $\langle 7\sqcup 1\langle 2\sqcup 1\langle 11\rangle\rangle\rangle$ whose realizability was unknown.
Keywords:
real algebraic curve.
@article{FAA_2002_36_3_a14,
author = {S. Yu. Orevkov},
title = {New $M${-Curve} of {Degree} 8},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {90--93},
year = {2002},
volume = {36},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a14/}
}
S. Yu. Orevkov. New $M$-Curve of Degree 8. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 90-93. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a14/
[1] Shevale B., “Chetyre $M$-krivye stepeni 8”, Funkts. analiz i ego pril., 36:1 (2002), 90–93 | DOI | MR
[2] Korchagin A. B., “The first part of Hilbert's sixteenth problem: history and main results”, Math. Series, 19, Texas Tech. University, 1997, 85–140
[3] Orevkov S. Yu., “Classification of Flexible $M$-curves of Degree 8 up to Isotopy”, Geom. Funct. Anal. (to appear) | MR
[4] Shustin E. I., Algebra i analiz, 11:5 (1999), 221–249 | MR
[5] Viro O. Ya., Veschestvennye algebraicheskie mnogoobraziya s predpisannymi topologicheskimi svoistvami, Diss. d. f.-m. n., Leningrad, 1983 ; Patchworking real algebraic varieties, http://www.math.uu.se/oleg | MR
[6] Viro O. Ya., Algebra i analiz, 1:5 (1989), 1–73 | MR | Zbl