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Journal of Mathematical Sciences

, Volume 131, Issue 1, pp 5366–5380 | Cite as

Patchworking Singularities Aμ and Dμ and Meanders of Their Smoothings

  • A. B. Korchagin
  • D. E. Smith
Article

Abstract

Let an algebraic curve f have a singular point of type Aμ or Dμ. Let \({\tilde f}\) be the curve obtained by smoothing the singular point of f. In this paper, local maximal meanders appearing under an M-smoothing in a neighborhood of the singular point are studied. A local maximal meander means that the number of real points of the intersection of \({\tilde f}\) with a coordinate axis in the neighborhood is maximal and the points belong to one of the components of \({\tilde f}\). An M-smoothing means that the number of components of \({\tilde f}\) which appear in the neighborhood under the smoothing is also maximal. Bibliography: 9 titles.

Keywords

Singular Point Coordinate Axis Algebraic Curve Real Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. B. Korchagin
    • 1
  • D. E. Smith
    • 1
  1. 1.Department of Mathematics and Statistics Texas Tech UniversityLubbockUSA

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