Restrictions on arrangements of ovals of projective algebraic curves of odd degree

Author:
Anatoly B. Korchagin

Journal:
Proc. Amer. Math. Soc. **129** (2001), 363-370

MSC (2000):
Primary 14P25; Secondary 14H50, 14P05

DOI:
https://doi.org/10.1090/S0002-9939-00-05568-4

Published electronically:
August 30, 2000

MathSciNet review:
1707523

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper investigates the first part of Hilbert's 16th problem which asks about topology of the real projective algebraic curves. Using the Rokhlin-Viro-Fiedler method of complex orientation, we obtain new restrictions on the arrangements of ovals of projective algebraic curves of odd degree , , with nests of depth .

**[F]**T. Fiedler,*Pencils of lines and topology of real algebraic curves*, Math. USSR-Izv.,**46**(1982), 853-863. MR**84e:14019****[H]**A. Harnack,*Uber die Vieltheiligkeit der ebenen algebraischen Kurven*, Math. Ann.**10**(1876), 189-199.**[K]**A. B. Korchagin,*M-curves of degree 9: new restrictions*, Math. Notes.**39**(1986), no. 2, 277-283. MR**87j:14054****[R]**V. A. Rokhlin,*Complex topological characteristics of real algebraic curves*, Uspekhi Mat. Nauk,**33**(1978), no. 5, 77-89; English transl. in Russian Math. Survey,**33**(1979). MR**81m:14024****[V1]**O. Ya. Viro,*Achievements in the topology of real algebraic varieties over the last six years*, Russian Math. Surveys,**41**(1986), 52-82. MR**87m:14023****[V2]**O. Ya. Viro,*Real plane algebraic curves: construction with controlled topology*, Leningrad Math. J.,**1**(1990), no. 5, 1059-1134. MR**91b:14078**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
14P25,
14H50,
14P05

Retrieve articles in all journals with MSC (2000): 14P25, 14H50, 14P05

Additional Information

**Anatoly B. Korchagin**

Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042

Email:
korchag@math.ttu.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05568-4

Keywords:
Complex orientations of algebraic curves,
positive and negative ovals,
positive and negative injective pairs,
chains of ovals

Received by editor(s):
April 14, 1998

Received by editor(s) in revised form:
May 4, 1999

Published electronically:
August 30, 2000

Communicated by:
Leslie Saper

Article copyright:
© Copyright 2000
American Mathematical Society