Infinite families of inequivalent real circle actions on affine four-space

Lucy Moser-Jauslin (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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 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 O2(C)-vector bundles.

Mots clés: Real forms; Circle actions; Non-linearizable actions

Domaines: Géométrie algébrique [math.AG]

Lucy Moser-Jauslin. Infinite families of inequivalent real circle actions on affine four-space. 2018. ⟨hal-01826458v1⟩