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


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.


Singular Point Coordinate Axis Algebraic Curve Real Point 
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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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