On the Jacobian Newton polygon of plane curve singularities |
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Authors: | Andrzej Lenarcik |
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Institution: | (1) Department of Mathematics, Technical University, Al. 1000 L PP7, 25-314 Kielce, Poland |
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Abstract: | We investigate the Jacobian Newton polygon of plane curve singularities. This invariant was introduced by Teissier in the
more general context of hypersurfaces. The Jacobian Newton polygon determines the topological type of a branch (Merle’s result)
but not of an arbitrary reduced curve (Eggers example). Our main result states that the Jacobian Newton Polygon determines
the topological type of a non-degenerate unitangent singularity. The Milnor number, the Łojasiewicz exponent, the Hironaka
exponent of maximal contact and the number of tangents are examples of invariants that can be calculated by means of the Jacobian
Newton polygon. We show that the number of branches and the Newton number defined by Oka do not have this property.
Dedicated to Professor Arkadiusz Płoski on his 60th birthday |
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Keywords: | Primary 32S55 Secondary 14H20 |
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