Modified Derksen invariant
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866912148530135040 |
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| author | Boldyrev, Ilya Gaifullin, Sergey Shafarevich, Anton |
| author_facet | Boldyrev, Ilya Gaifullin, Sergey Shafarevich, Anton |
| contents | Modified Derksen invariant HD*(X) of an affine variety X is a subalgebra in K[X] generated by kernels of all locally nilpotent derivations of K[X] with slices. If there is a locally nilpotent derivation of K[X] with a slice then X is a product of Y and a line, where Y is an affine variety. We prove that there are three possibilities: A) HD*(X) = K[X]; B) HD*(X) is a proper infintely generated subalgebra; C) HD*(X) = \BK[Y]. We give examples for each case, and also provide sufficient conditions for the variety Y so that the variety X belongs to one of the type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08421 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modified Derksen invariant Boldyrev, Ilya Gaifullin, Sergey Shafarevich, Anton Algebraic Geometry Primary 14R05, 14R20, Secondary 14A05, 13A50 Modified Derksen invariant HD*(X) of an affine variety X is a subalgebra in K[X] generated by kernels of all locally nilpotent derivations of K[X] with slices. If there is a locally nilpotent derivation of K[X] with a slice then X is a product of Y and a line, where Y is an affine variety. We prove that there are three possibilities: A) HD*(X) = K[X]; B) HD*(X) is a proper infintely generated subalgebra; C) HD*(X) = \BK[Y]. We give examples for each case, and also provide sufficient conditions for the variety Y so that the variety X belongs to one of the type. |
| title | Modified Derksen invariant |
| topic | Algebraic Geometry Primary 14R05, 14R20, Secondary 14A05, 13A50 |
| url | https://arxiv.org/abs/2312.08421 |