Locally Nilpotent Derivations of Graded Integral Domains and Cylindricity
| العنوان: | Locally Nilpotent Derivations of Graded Integral Domains and Cylindricity |
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| المؤلفون: | Michael Chitayat, Daniel Daigle |
| المصدر: | Transformation Groups. |
| بيانات النشر: | Springer Science and Business Media LLC, 2022. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Algebra and Number Theory, FOS: Mathematics, Geometry and Topology, Commutative Algebra (math.AC), Mathematics - Commutative Algebra, Primary: 13N15, 14R20. Secondary: 14C20, 14R05, 14R25, Algebraic Geometry (math.AG) |
| الوصف: | Let B be a commutative $\mathbb{Z}$-graded domain of characteristic zero. An element f of B is said to be cylindrical if it is nonzero, homogeneous of nonzero degree, and such that $B_{(f)}$ is a polynomial ring in one variable over a subring. We study the relation between the existence of a cylindrical element of B and the existence of a nonzero locally nilpotent derivation of B. Also, given d > 0, we give sufficient conditions that guarantee that every derivation of $B^{(d)} = \oplus_i B_{di}$ can be extended to a derivation of B. We generalize some results of Kishimoto, Prokhorov and Zaidenberg that relate the cylindricity of a polarized projective variety (Y,H) to the existence of a nontrivial G_a-action on the affine cone over (Y,H). 27 pages |
| تدمد: | 1531-586X 1083-4362 |
| DOI: | 10.1007/s00031-022-09753-5 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f29d99bac9eed8debe78f3f554f97ba5 https://doi.org/10.1007/s00031-022-09753-5 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....f29d99bac9eed8debe78f3f554f97ba5 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 1531586X 10834362 |
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| DOI: | 10.1007/s00031-022-09753-5 |