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arXiv · 2410.00793

The value semigroup of a plane curve singularity with several branches

M. D'Anna·F. Delgado·L. Guerrieri·N. Maugeri·V. Micale
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Abstract

We present a constructive procedure, based on the notion of Ap\'ery set, to obtain the value semigroup of a plane curve singularity from the value semigroup of its blow-up and viceversa. In particular we give a blow-down process that allows to reconstruct a plane algebroid curve form its blow-up, even if it is not local. Then we characterize numerically all the possible multiplicity trees of plane curve singularities, obtaining in this way a constructive description of all their value semigroups.

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M. D'Anna, F. Delgado, L. Guerrieri, N. Maugeri, V. Micale. 2024-10-01. The value semigroup of a plane curve singularity with several branches. https://arxiv.org/abs/2410.00793

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