Exceptional Algebraic Sets for Infinite Discrete Groups of \(PSL(3,\mathbb {C})\)

Abstract

In this note we show that the exceptional algebraic set for an infinite discrete group in \(PSL(3,{{\mathbb {C}}})\) should be a finite union of: complex lines, copies of the Veronese curve or copies of the cubic \(xy^2-z^3\).

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Acknowledgements

The authors would like to thank to the UCIM UNAM and their people for its hospitality and kindness during the writing of this paper. We also grateful to J. F. Estrada and J. J. Zacarías for fruitful conversations.

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Correspondence to Luis Loeza.

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Partially supported by grants of projects PAPIIT UNAM: IN110219.

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Loeza, L., Cano, A. Exceptional Algebraic Sets for Infinite Discrete Groups of \(PSL(3,\mathbb {C})\). Bull Braz Math Soc, New Series (2020). https://doi.org/10.1007/s00574-020-00218-5

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Keywords

  • Complex Kleinian groups
  • Exceptional algebraic set
  • Veronese groups.

Mathematics Subject Classification

  • Primary 37F99
  • Secondary 30F40
  • 20H10
  • 57M60