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On the semigroup of an ordinary multiple point

Published online by Cambridge University Press:  17 April 2009

Devadatta M. Kulkarni
Affiliation:
Department of Mathematical, Sciences Oakland University, Rochester MI 48063, United States of America
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Abstract

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In this paper we define the semigroup of an ordinary multiple point of an analytic plane curve f. This semigroup on tuples of integers is completely characterised in terms of the order of f, that is the number of distinct tangent directions to f at that point.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Abhyankar, S., ‘On the semigroup of meromorphic curve”, (Part I), in International Symposium on Algebraic Geometry, Kyoto, pp. 249414., 1977.Google Scholar
[2]Angermüller, G., ‘Die Werthalbgruppe einer Ebenen Irreduziblen Algebroiden Kurve”, Math. Z. 153 (1977), 267282.Google Scholar
[3]Bayer, V., ‘Semigroup of two irreducible algebroid plane curves’, Manuscripta Math. 49 (1985), 207241.Google Scholar
[4]Garcia, A., ‘Semigroups associated to singular points of plane curves’, J. Reine Angew. Math. 336 (1982), 165185.Google Scholar