Automorphisms and Twisted Forms of Rings of Invariants

János Kollár

doi:10.1007/s00032-024-00403-x

Automorphisms and Twisted Forms of Rings of Invariants

János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let G⊂GL_n(k) be a finite subgroup and k[x1,⋯,xn]^G⊂k[x₁,⋯,x_n] its ring of invariants. We show that, in many cases, the automorphism group of k[x1,⋯,xn]^G is k^×.

Original language	English (US)
Journal	Milan Journal of Mathematics
DOIs	https://doi.org/10.1007/s00032-024-00403-x
State	Accepted/In press - 2024

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Automorphism
Birational rigidity
Ring of invariants
Twisted forms

Access to Document

10.1007/s00032-024-00403-x

Cite this

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title = "Automorphisms and Twisted Forms of Rings of Invariants",

abstract = "Let G⊂GLn(k) be a finite subgroup and k[x1,⋯,xn]G⊂k[x1,⋯,xn] its ring of invariants. We show that, in many cases, the automorphism group of k[x1,⋯,xn]G is k×.",

keywords = "Automorphism, Birational rigidity, Ring of invariants, Twisted forms",

author = "J{\'a}nos Koll{\'a}r",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Seminario Matematico e Fisico di Milano 2024.",

year = "2024",

doi = "10.1007/s00032-024-00403-x",

language = "English (US)",

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T1 - Automorphisms and Twisted Forms of Rings of Invariants

AU - Kollár, János

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Seminario Matematico e Fisico di Milano 2024.

PY - 2024

Y1 - 2024

N2 - Let G⊂GLn(k) be a finite subgroup and k[x1,⋯,xn]G⊂k[x1,⋯,xn] its ring of invariants. We show that, in many cases, the automorphism group of k[x1,⋯,xn]G is k×.

AB - Let G⊂GLn(k) be a finite subgroup and k[x1,⋯,xn]G⊂k[x1,⋯,xn] its ring of invariants. We show that, in many cases, the automorphism group of k[x1,⋯,xn]G is k×.

KW - Automorphism

KW - Birational rigidity

KW - Ring of invariants

KW - Twisted forms

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M3 - Article

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SN - 1424-9286

JO - Milan Journal of Mathematics

JF - Milan Journal of Mathematics

ER -

Automorphisms and Twisted Forms of Rings of Invariants

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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