Stillman's question for twisted commutative algebras
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2020
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913434759593984 |
|---|---|
| author | Ganapathy, Karthik |
| author_facet | Ganapathy, Karthik |
| contents | Let $\mathbf{A}_{n, m}$ be the polynomial ring $\text{Sym}(\mathbf{C}^n \otimes \mathbf{C}^m)$ with the natural action of $\mathbf{GL}_m(\mathbf{C})$. We construct a family of $\mathbf{GL}_m(\mathbf{C})$-stable ideals $J_{n, m}$ in $\mathbf{A}_{n, m}$, each equivariantly generated by one homogeneous polynomial of degree $2$. Using the Ananyan-Hochster principle, we show that the regularity of this family is unbounded. This negatively answers a question raised by Erman-Sam-Snowden on a generalization of Stillman's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_03038 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Stillman's question for twisted commutative algebras Ganapathy, Karthik Commutative Algebra 13D02, 13A50 Let $\mathbf{A}_{n, m}$ be the polynomial ring $\text{Sym}(\mathbf{C}^n \otimes \mathbf{C}^m)$ with the natural action of $\mathbf{GL}_m(\mathbf{C})$. We construct a family of $\mathbf{GL}_m(\mathbf{C})$-stable ideals $J_{n, m}$ in $\mathbf{A}_{n, m}$, each equivariantly generated by one homogeneous polynomial of degree $2$. Using the Ananyan-Hochster principle, we show that the regularity of this family is unbounded. This negatively answers a question raised by Erman-Sam-Snowden on a generalization of Stillman's conjecture. |
| title | Stillman's question for twisted commutative algebras |
| topic | Commutative Algebra 13D02, 13A50 |
| url | https://arxiv.org/abs/2007.03038 |