Two Criteria For Quasihomogeneity
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_ | 1866929203911327744 |
|---|---|
| author | Maitra, Sarasij Mukundan, Vivek |
| author_facet | Maitra, Sarasij Mukundan, Vivek |
| contents | Let $(R,\mathfrak{m}_R,k)$ be a one-dimensional complete local reduced $k$-algebra over a field of characteristic zero. The ring $R$ is said to be quasihomogeneous if there exists a surjection $Ω_R\twoheadrightarrow \mathfrak{m}$ where $Ω_R$ denotes the module of differentials. We present two characterizations of quasihomogeneity of $R$ in the situation when $R$ is a domain: the first one on the valuation semigroup of $R$ and the other on the trace ideal of the module $Ω_R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04254 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two Criteria For Quasihomogeneity Maitra, Sarasij Mukundan, Vivek Commutative Algebra Algebraic Geometry 13A15 (Primary), 13H05 (Secondary) Let $(R,\mathfrak{m}_R,k)$ be a one-dimensional complete local reduced $k$-algebra over a field of characteristic zero. The ring $R$ is said to be quasihomogeneous if there exists a surjection $Ω_R\twoheadrightarrow \mathfrak{m}$ where $Ω_R$ denotes the module of differentials. We present two characterizations of quasihomogeneity of $R$ in the situation when $R$ is a domain: the first one on the valuation semigroup of $R$ and the other on the trace ideal of the module $Ω_R$. |
| title | Two Criteria For Quasihomogeneity |
| topic | Commutative Algebra Algebraic Geometry 13A15 (Primary), 13H05 (Secondary) |
| url | https://arxiv.org/abs/2401.04254 |