PATCHWORKING SINGULARITIES Aμ AND Dμ AND MEANDERS OF THEIR SMOOTHINGS


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Abstract

Let an algebraic curve f have a singular point of type Aμ or D. Let 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 f with a coordinate axis in the neighborhood is maximal and the points belong to one of the components of f. An M-smoothing means that the number of components of f which appear in the neighborhood under the smoothing is also maximal. Bibliography: 9 titles.

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