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The value semigroup of a plane curve singularity with several branches
Journal
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
100
Author
D’Anna Marco
Delgado de la Mata Félix
Guerrieri Lorenzo
Maugeri Nicola
Micale Vincenzo
Volume
35
Number
3
Pages
459–499
ISSN
1120-6330
Keywords in English
good semigroup
Apéry set
plane curve singularity
multiplicity tree
Access date
2025-07-01
Language
English
Journal language
English
Abstract in English
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 vice-versa. In particular, we give a blow-down process that allows us 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.
Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
| dc.abstract.en | 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 vice-versa. In particular, we give a blow-down process that allows us 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. | |
| dc.affiliation | Wydział Matematyki i Informatyki : Instytut Matematyki | |
| dc.contributor.author | D’Anna, Marco | |
| dc.contributor.author | Delgado de la Mata, Félix | |
| dc.contributor.author | Guerrieri, Lorenzo - 428412 | |
| dc.contributor.author | Maugeri, Nicola | |
| dc.contributor.author | Micale, Vincenzo | |
| dc.date.accession | 2025-07-01 | |
| dc.date.accessioned | 2025-07-01T14:00:52Z | |
| dc.date.available | 2025-07-01T14:00:52Z | |
| dc.date.createdat | 2025-07-01T07:56:12Z | en |
| dc.date.issued | 2024 | |
| dc.date.openaccess | 0 | |
| dc.description.accesstime | w momencie opublikowania | |
| dc.description.number | 3 | |
| dc.description.physical | 459–499 | |
| dc.description.version | ostateczna wersja wydawcy | |
| dc.description.volume | 35 | |
| dc.identifier.doi | 10.4171/RLM/1048 | |
| dc.identifier.issn | 1120-6330 | |
| dc.identifier.project | PN/PPO/2018/1/00013/U/00001 | |
| dc.identifier.project | DRC AI | |
| dc.identifier.uri | https://ruj.uj.edu.pl/handle/item/554167 | |
| dc.identifier.weblink | https://ems.press/content/serial-article-files/50733 | |
| dc.language | eng | |
| dc.language.container | eng | |
| dc.rights | Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa | |
| dc.rights.licence | CC-BY | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/legalcode.pl | |
| dc.share.type | inne | |
| dc.source.integrator | false | |
| dc.subject.en | good semigroup | |
| dc.subject.en | Apéry set | |
| dc.subject.en | plane curve singularity | |
| dc.subject.en | multiplicity tree | |
| dc.subtype | Article | |
| dc.title | The value semigroup of a plane curve singularity with several branches | |
| dc.title.journal | Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni | |
| dc.type | JournalArticle | |
| dspace.entity.type | Publication | en |
dc.abstract.en
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 vice-versa. In particular, we give a blow-down process that allows us 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. dc.affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki dc.contributor.author
D’Anna, Marco dc.contributor.author
Delgado de la Mata, Félix dc.contributor.author
Guerrieri, Lorenzo - 428412 dc.contributor.author
Maugeri, Nicola dc.contributor.author
Micale, Vincenzo dc.date.accession
2025-07-01 dc.date.accessioned
2025-07-01T14:00:52Z dc.date.available
2025-07-01T14:00:52Z dc.date.createdaten
2025-07-01T07:56:12Z dc.date.issued
2024 dc.date.openaccess
0 dc.description.accesstime
w momencie opublikowania dc.description.number
3 dc.description.physical
459–499 dc.description.version
ostateczna wersja wydawcy dc.description.volume
35 dc.identifier.doi
10.4171/RLM/1048 dc.identifier.issn
1120-6330 dc.identifier.project
PN/PPO/2018/1/00013/U/00001 dc.identifier.project
DRC AI dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/554167 dc.identifier.weblink
https://ems.press/content/serial-article-files/50733 dc.language
eng dc.language.container
eng dc.rights
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa dc.rights.licence
CC-BY dc.rights.uri
http://creativecommons.org/licenses/by/4.0/legalcode.pl dc.share.type
inne dc.source.integrator
false dc.subject.en
good semigroup dc.subject.en
Apéry set dc.subject.en
plane curve singularity dc.subject.en
multiplicity tree dc.subtype
Article dc.title
The value semigroup of a plane curve singularity with several branches dc.title.journal
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni dc.type
JournalArticle dspace.entity.typeen
Publication Affiliations
No affiliation
D’Anna, Marco
Delgado de la Mata, Félix
Maugeri, Nicola
Micale, Vincenzo
Wydział Matematyki i Informatyki
Guerrieri, Lorenzo
mathematics
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