The value semigroup of a plane curve singularity with several branches
Abstract
We present a constructive procedure, based on the notion of Apéry 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2024
- DOI:
- 10.48550/arXiv.2410.00793
- arXiv:
- arXiv:2410.00793
- Bibcode:
- 2024arXiv241000793D
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14H20;
- 14H50;
- 13H15;
- 20M14
- E-Print:
- 38 pages, 4 figures