The value semigroup of a plane curve singularity with several branches
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913525637578752 |
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| author | D'Anna, M. Delgado, F. Guerrieri, L. Maugeri, N. Micale, V. |
| author_facet | D'Anna, M. Delgado, F. Guerrieri, L. Maugeri, N. Micale, V. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The value semigroup of a plane curve singularity with several branches D'Anna, M. Delgado, F. Guerrieri, L. Maugeri, N. Micale, V. Algebraic Geometry 14H20, 14H50, 13H15, 20M14 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. |
| title | The value semigroup of a plane curve singularity with several branches |
| topic | Algebraic Geometry 14H20, 14H50, 13H15, 20M14 |
| url | https://arxiv.org/abs/2410.00793 |