Conductors of Abhyankar-Moh semigroups of even degrees
In their paper on the embeddings of the line in the plane, Abhyankar and Moh proved an important inequality, now known as the Abhyankar-Moh inequality, which can be stated in terms of the semigroup associated with the branch at infinity of a plane algebraic curve. Barrolleta, García Barroso and Płos...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-02-01
|
| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023113?viewType=HTML |
| _version_ | 1797833218393636864 |
|---|---|
| author | Evelia R. GARCÍA BARROSO Juan Ignacio GARCÍA-GARCÍA Luis José SANTANA SÁNCHEZ Alberto VIGNERON-TENORIO |
| author_facet | Evelia R. GARCÍA BARROSO Juan Ignacio GARCÍA-GARCÍA Luis José SANTANA SÁNCHEZ Alberto VIGNERON-TENORIO |
| author_sort | Evelia R. GARCÍA BARROSO |
| collection | DOAJ |
| description | In their paper on the embeddings of the line in the plane, Abhyankar and Moh proved an important inequality, now known as the Abhyankar-Moh inequality, which can be stated in terms of the semigroup associated with the branch at infinity of a plane algebraic curve. Barrolleta, García Barroso and Płoski studied the semigroups of integers satisfying the Abhyankar-Moh inequality and call them Abhyankar-Moh semigroups. They described such semigroups with the maximum conductor. In this paper we prove that all possible conductor values are achieved for the Abhyankar-Moh semigroups of even degree. Our proof is constructive, explicitly describing families that achieve a given value as its conductor. |
| first_indexed | 2024-04-09T14:19:49Z |
| format | Article |
| id | doaj.art-a167237d5e884656b0e122aac4558d79 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-09T14:19:49Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-a167237d5e884656b0e122aac4558d792023-05-05T01:40:04ZengAIMS PressElectronic Research Archive2688-15942023-02-013142213222910.3934/era.2023113Conductors of Abhyankar-Moh semigroups of even degreesEvelia R. GARCÍA BARROSO 0Juan Ignacio GARCÍA-GARCÍA1Luis José SANTANA SÁNCHEZ2Alberto VIGNERON-TENORIO 31. Departamento de Matemáticas, Estadística e I.O. Sección de Matemáticas, Universidad de La Laguna. Apartado de Correos 456. 38200 La Laguna, Tenerife, Spain2. Departamento de Matemáticas/INDESS (Instituto Universitario para el Desarrollo Social Sostenible). Universidad de Cádiz. E-11510 Puerto Real, Cádiz, Spain1. Departamento de Matemáticas, Estadística e I.O. Sección de Matemáticas, Universidad de La Laguna. Apartado de Correos 456. 38200 La Laguna, Tenerife, Spain3. Departamento de Matemáticas/INDESS (Instituto Universitario para el Desarrollo Social Sostenible). Universidad de Cádiz. E-11406 Jerez de la Frontera, Cádiz, SpainIn their paper on the embeddings of the line in the plane, Abhyankar and Moh proved an important inequality, now known as the Abhyankar-Moh inequality, which can be stated in terms of the semigroup associated with the branch at infinity of a plane algebraic curve. Barrolleta, García Barroso and Płoski studied the semigroups of integers satisfying the Abhyankar-Moh inequality and call them Abhyankar-Moh semigroups. They described such semigroups with the maximum conductor. In this paper we prove that all possible conductor values are achieved for the Abhyankar-Moh semigroups of even degree. Our proof is constructive, explicitly describing families that achieve a given value as its conductor.https://www.aimspress.com/article/doi/10.3934/era.2023113?viewType=HTMLabhyankar-moh inequalityabhyankar-moh semigroupsconductorgluing of semigroupsbranch at infinity |
| spellingShingle | Evelia R. GARCÍA BARROSO Juan Ignacio GARCÍA-GARCÍA Luis José SANTANA SÁNCHEZ Alberto VIGNERON-TENORIO Conductors of Abhyankar-Moh semigroups of even degrees Electronic Research Archive abhyankar-moh inequality abhyankar-moh semigroups conductor gluing of semigroups branch at infinity |
| title | Conductors of Abhyankar-Moh semigroups of even degrees |
| title_full | Conductors of Abhyankar-Moh semigroups of even degrees |
| title_fullStr | Conductors of Abhyankar-Moh semigroups of even degrees |
| title_full_unstemmed | Conductors of Abhyankar-Moh semigroups of even degrees |
| title_short | Conductors of Abhyankar-Moh semigroups of even degrees |
| title_sort | conductors of abhyankar moh semigroups of even degrees |
| topic | abhyankar-moh inequality abhyankar-moh semigroups conductor gluing of semigroups branch at infinity |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023113?viewType=HTML |
| work_keys_str_mv | AT eveliargarciabarroso conductorsofabhyankarmohsemigroupsofevendegrees AT juanignaciogarciagarcia conductorsofabhyankarmohsemigroupsofevendegrees AT luisjosesantanasanchez conductorsofabhyankarmohsemigroupsofevendegrees AT albertovignerontenorio conductorsofabhyankarmohsemigroupsofevendegrees |