A Geometric description of almost Gorensteinness for two-dimensional normal singularities
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913569009827840 |
|---|---|
| author | Okuma, Tomohiro Watanabe, Kei-ichi Yoshida, Ken-ichi |
| author_facet | Okuma, Tomohiro Watanabe, Kei-ichi Yoshida, Ken-ichi |
| contents | Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field. Then $A$ is called an elliptic singularity if $p_f(A)=1$, where $p_f$ denotes the fundamental genus. On the other hand, the concept of almost Gorenstein rings was introduced by Barucci and Fröberg for one-dimensional local rings and generalized by Goto, Takahashi and Taniguchi to higher dimension. In this paper, we describe almost Gorenstein rings in geometric language using resolution of singularities and give criterions to be almost Gorenstein. In particular, we show that elliptic singularities are almost Gorenstein. Also, for every integer $g\ge 2$, we provide examples of singularities that is almost Gorenstein (resp. not almost Gorenstein) with $p_f(A)=g$. We also provide several examples of determinantal singularities associated with $2\times 3$ matrices, which include both almost Gorenstein singularities and non-almost Gorenstein singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Geometric description of almost Gorensteinness for two-dimensional normal singularities Okuma, Tomohiro Watanabe, Kei-ichi Yoshida, Ken-ichi Commutative Algebra 13H10, 13G05, 14B05, 14J17 Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field. Then $A$ is called an elliptic singularity if $p_f(A)=1$, where $p_f$ denotes the fundamental genus. On the other hand, the concept of almost Gorenstein rings was introduced by Barucci and Fröberg for one-dimensional local rings and generalized by Goto, Takahashi and Taniguchi to higher dimension. In this paper, we describe almost Gorenstein rings in geometric language using resolution of singularities and give criterions to be almost Gorenstein. In particular, we show that elliptic singularities are almost Gorenstein. Also, for every integer $g\ge 2$, we provide examples of singularities that is almost Gorenstein (resp. not almost Gorenstein) with $p_f(A)=g$. We also provide several examples of determinantal singularities associated with $2\times 3$ matrices, which include both almost Gorenstein singularities and non-almost Gorenstein singularities. |
| title | A Geometric description of almost Gorensteinness for two-dimensional normal singularities |
| topic | Commutative Algebra 13H10, 13G05, 14B05, 14J17 |
| url | https://arxiv.org/abs/2410.23911 |