A note on homogeneous rank $2$ locally nilpotent derivations on $k[X,Y,Z]$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909143885938688 |
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| author | Ghosh, Parnashree |
| author_facet | Ghosh, Parnashree |
| contents | In this article we show that for every prime number $p$, any irreducible homogeneous locally nilpotent derivations of rank $2$ and degree $p-2$ are triangularizable. Further, we describe the structure of irreducible non-triangularizable homogeneous locally nilpotent derivations of rank $2$ and degree $pq-2$, where $p,q$ are prime numbers. Consequently, we give explicit descriptions of the generators of the image ideals of certain homogeneous locally nilpotent derivations of rank $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_05906 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A note on homogeneous rank $2$ locally nilpotent derivations on $k[X,Y,Z]$ Ghosh, Parnashree Commutative Algebra 13N15, 13F20 In this article we show that for every prime number $p$, any irreducible homogeneous locally nilpotent derivations of rank $2$ and degree $p-2$ are triangularizable. Further, we describe the structure of irreducible non-triangularizable homogeneous locally nilpotent derivations of rank $2$ and degree $pq-2$, where $p,q$ are prime numbers. Consequently, we give explicit descriptions of the generators of the image ideals of certain homogeneous locally nilpotent derivations of rank $2$. |
| title | A note on homogeneous rank $2$ locally nilpotent derivations on $k[X,Y,Z]$ |
| topic | Commutative Algebra 13N15, 13F20 |
| url | https://arxiv.org/abs/2206.05906 |