The main result of this article is to construct infinite families of non-equivalent equivariant real forms of linear C*-actions on affine four-space. We consider the real form of $\mathbb{C}^*$ whose fixed point is a circle. In [F-MJ] one example of a non-linearizable circle action was constructed. Here, this result is generalized by developing a new approach which allows us to compare different real forms. The constructions of these forms are based on the structure of equivariant $\mathrm{O}_2(\mathbb{C})$-vector bundles.

Source : oai:HAL:hal-01826458v2

Volume: Volume 3

Published on: March 1, 2019

Submitted on: July 16, 2018

Keywords: real affine varieties,non-linearizable actions,circle actions,Real forms,2010 MSC: 14L30; 14R20; 14P99,
[
MATH.MATH-AG
]
Mathematics [math]/Algebraic Geometry [math.AG]

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