Título:
On polynomial automorphisms commuting with a simple derivation
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Autor:
Montagard, Pierre-Louis
Pan, Iván
Rittatore, Álvaro
Pan, Iván
Rittatore, Álvaro
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Tipo de documento:
Preprint
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MATHEMATICS - ALGEBRAIC GEOMETRY
MATHEMATICS - COMMUTATIVE ALGEBRA
MATHEMATICS - COMMUTATIVE ALGEBRA
Año de publicación:
2024
Contenido:
Resumen:
Let D be a simple derivation of the polynomial ring k[x1,…,xn], where k is an algebraically closed field of characteristic zero, and denote by Aut(D)⊂Aut(k[x1,…,xn]) the subgroup of k-automorphisms commuting with D. We show that the connected component of Aut(D) passing through the identity is a unipotent algebraic group of dimension at most n−2, this bound being sharp. Moreover, Aut(D) is an algebraic group if and only if it is a connected ind-group. Given a simple derivation D, we characterize when Aut(D) contains a normal subgroup of translations. As an application of our techniques we show that if n=3, then either Aut(D) is a discrete group or it is isomorphic to the additive group acting by translations, and give some insight on the case n=4.
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Publicado también en: HAL, 2024, 1-15. Id: ID: hal-04840230
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arXiv
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Mathematics (Algebraic Geometry), arXiv:2412.09519v1, dic. 2024, pp.1-15
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Citación:
Montagard, P, Pan, I y Rittatore, Á. "On polynomial automorphisms commuting with a simple derivation" [Preprint]. Publicado en: Mathematics (Algebraic Geometry). 2024, arXiv:2412.09519v1, dic. 202, pp.1-15 h. DOI: 10.48550/arXiv.2412.09519
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2412.09519v1.pdf | — | 225.48 KB | Adobe PDF |