## Lucy Moser-Jauslin - Infinite families of inequivalent real circle actions on affine four-space

epiga:4685 - Épijournal de Géométrie Algébrique, March 1, 2019, Volume 3 - https://doi.org/10.46298/epiga.2019.volume3.4685
Infinite families of inequivalent real circle actions on affine four-space

Authors: Lucy Moser-Jauslin

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.

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]