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Quotients and invariants of \(\mathcal {AS}\)-sets equipped with a finite group action

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Abstract

Using the geometric quotient of a real algebraic set by the action of a finite group G, we construct invariants of G-affine real algebraic varieties with respect to equivariant homeomorphisms with algebraic graph, including additive invariants with values in \({\mathbb {Z}}\). The construction requires to consider the wider category of \(\mathcal {AS}\)-sets.

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Acknowledgements

The author wishes to thank J.-B. Campesato, G. Fichou and A. Parusiński for useful discussions and comments.

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Authors and Affiliations

  1. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

    Fabien Priziac

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  1. Fabien Priziac
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Correspondence to Fabien Priziac.

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Communicated by Jean-Yves Welschinger.

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Priziac, F. Quotients and invariants of \(\mathcal {AS}\)-sets equipped with a finite group action. Math. Ann. 377, 1015–1055 (2020). https://doi.org/10.1007/s00208-020-01994-7

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  • DOI: https://doi.org/10.1007/s00208-020-01994-7

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