Limit points and additive group actions

Fuente: arXiv
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Main Author: Arzhantsev, Ivan
Format: Preprint
Published: 2021
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author Arzhantsev, Ivan
author_facet Arzhantsev, Ivan
contents We show that an effective action of the one-dimensional torus $\mathbb{G}_m$ on a normal affine algebraic variety $X$ can be extended to an effective action of a semi-direct product $\mathbb{G}_m\rightthreetimes\mathbb{G}_a$ with the same general orbit closures if and only if there is a divisor $D$ on $X$ that consists of $\mathbb{G}_m$-fixed points. This result is applied to the study of orbits of the automorphism group $\text{Aut}(X)$ on $X$.
format Preprint
id arxiv_https___arxiv_org_abs_2102_11330
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Limit points and additive group actions
Arzhantsev, Ivan
Algebraic Geometry
Commutative Algebra
Primary 14J50, 14R20, Secondary 13A50, 14L30
We show that an effective action of the one-dimensional torus $\mathbb{G}_m$ on a normal affine algebraic variety $X$ can be extended to an effective action of a semi-direct product $\mathbb{G}_m\rightthreetimes\mathbb{G}_a$ with the same general orbit closures if and only if there is a divisor $D$ on $X$ that consists of $\mathbb{G}_m$-fixed points. This result is applied to the study of orbits of the automorphism group $\text{Aut}(X)$ on $X$.
title Limit points and additive group actions
topic Algebraic Geometry
Commutative Algebra
Primary 14J50, 14R20, Secondary 13A50, 14L30
url https://arxiv.org/abs/2102.11330