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Patchworking Singularities A μ and D μ and Meanders of Their Smoothings

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics Texas Tech University, Lubbock, TX, 79409-1042, USA

    A. B. Korchagin & D. E. Smith

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  1. A. B. Korchagin
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  2. D. E. Smith
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 193–217.

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Korchagin, A.B., Smith, D.E. Patchworking Singularities A μ and D μ and Meanders of Their Smoothings. J Math Sci 131, 5366–5380 (2005). https://doi.org/10.1007/s10958-005-0409-3

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  • DOI: https://doi.org/10.1007/s10958-005-0409-3

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