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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
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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 $k$.


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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

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