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

Abstract : 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.
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  • HAL Id : hal-01826458, version 2
  • ARXIV : 1807.00524

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Lucy Moser-Jauslin. Infinite families of inequivalent real circle actions on affine four-space. Épijournal de Géométrie Algébrique, EPIGA, 2019, 3. ⟨hal-01826458v2⟩

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