Restrictions on arrangements of ovals of projective algebraic curves of odd degree
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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 $d = 4k + 1$, $k \geq 2$, with nests of depth $k$.References
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Additional Information
- Anatoly B. Korchagin
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042
- Email: korchag@math.ttu.edu
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1707523