Cylinders and the zero locus of the plinth ideal
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910183141146624 |
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| author | Shakhmatov, Kirill |
| author_facet | Shakhmatov, Kirill |
| contents | Given a $\mathbb{G}_\mathrm{a}$-action on an affine variety $X$, we show that the complement of the union of all principal invariant cylinders in $X$ is equal to the zero locus of the plinth ideal of the corresponding locally nilpotent derivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00138 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cylinders and the zero locus of the plinth ideal Shakhmatov, Kirill Algebraic Geometry 14R10, 14R20 (Primary) 13A50 (Secondary) Given a $\mathbb{G}_\mathrm{a}$-action on an affine variety $X$, we show that the complement of the union of all principal invariant cylinders in $X$ is equal to the zero locus of the plinth ideal of the corresponding locally nilpotent derivation. |
| title | Cylinders and the zero locus of the plinth ideal |
| topic | Algebraic Geometry 14R10, 14R20 (Primary) 13A50 (Secondary) |
| url | https://arxiv.org/abs/2605.00138 |