On $δ$-sequences and surfaces at infinity
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918433644347392 |
|---|---|
| author | Galindo, C. Monserrat, F. Moreno-Ávila, C. -J. Moyano-Fernández, J. -J. |
| author_facet | Galindo, C. Monserrat, F. Moreno-Ávila, C. -J. Moyano-Fernández, J. -J. |
| contents | In most cases the semigroup at infinity $S$ of a curve $C$ with only one place at infinity is generated by a $δ$-sequence. This sequence provides geometrical information on $C$ such as the dual graph of the resolution of the singularity of $C$ at infinity. Since different $δ$-sequences can generate the same semigroup, it is an interesting problem to know the geometrical behaviour of curves $C$ sharing the same semigroup $S$. An analogous problem arises in a more general context when considering surfaces at infinity and their $δ$-semigroups.
We show how to construct $δ$-sequences, and how to obtain different families that generate the same semigroup $S$, allowing us to study the geometrical content encoded by $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $δ$-sequences and surfaces at infinity Galindo, C. Monserrat, F. Moreno-Ávila, C. -J. Moyano-Fernández, J. -J. Algebraic Geometry Commutative Algebra Primary: 14J26, 14H20, Secondary: 32S05, 14H55 In most cases the semigroup at infinity $S$ of a curve $C$ with only one place at infinity is generated by a $δ$-sequence. This sequence provides geometrical information on $C$ such as the dual graph of the resolution of the singularity of $C$ at infinity. Since different $δ$-sequences can generate the same semigroup, it is an interesting problem to know the geometrical behaviour of curves $C$ sharing the same semigroup $S$. An analogous problem arises in a more general context when considering surfaces at infinity and their $δ$-semigroups. We show how to construct $δ$-sequences, and how to obtain different families that generate the same semigroup $S$, allowing us to study the geometrical content encoded by $S$. |
| title | On $δ$-sequences and surfaces at infinity |
| topic | Algebraic Geometry Commutative Algebra Primary: 14J26, 14H20, Secondary: 32S05, 14H55 |
| url | https://arxiv.org/abs/2408.15931 |