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European Journal of Mathematics

, Volume 5, Issue 3, pp 937–957 | Cite as

The fundamental group of a log terminal \(\mathbb {T}\)-variety

  • Antonio Laface
  • Alvaro Liendo
  • Joaquín MoragaEmail author
Research Article
  • 61 Downloads

Abstract

We introduce an approach to study the fundamental group of a log terminal \(\mathbb {T}\)-variety. As applications, we prove the simply connectedness of the spectrum of the Cox ring of a complex Fano variety, we compute the fundamental group of a rational log terminal \(\mathbb {T}\)-variety of complexity one, and we study the local fundamental group of a log terminal \(\mathbb {T}\)-singularity with a good torus action and trivial GIT decomposition.

Keywords

Torus actions Fundamental groups \(\mathbb {T}\)-varieties 

Mathematics Subject Classification

14M25 14C15 

Notes

Acknowledgements

The authors would like to thank János Kollár and Chenyang Xu for pointing out a gap in an early version. The authors would also like to thank Hendrik Süß for providing interesting examples. We would like to thank the anonymous referee whose comments helped to improve the presentation of the paper.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Antonio Laface
    • 1
  • Alvaro Liendo
    • 2
  • Joaquín Moraga
    • 3
    Email author
  1. 1.Departamento de MatemáticaUniversidad de ConcepciónConcepciónChile
  2. 2.Instituto de Matemática y FísicaUniversidad de TalcaTalcaChile
  3. 3.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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