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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Restrictions on arrangements of ovals of projective algebraic curves of odd degree
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by Anatoly B. Korchagin PDF
Proc. Amer. Math. Soc. 129 (2001), 363-370 Request permission

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
  • 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