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

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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.

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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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Correspondence to Joaquín Moraga.

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The first author was partially supported by Proyecto FONDECYT Regular No. 1150732 and Projecto Anillo ACT 1415 PIA Conicyt. The second author was partially supported by Proyecto FONDECYT Regular No. 1160864.

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Laface, A., Liendo, A. & Moraga, J. The fundamental group of a log terminal \(\mathbb {T}\)-variety. European Journal of Mathematics 5, 937–957 (2019). https://doi.org/10.1007/s40879-018-0296-z

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  • DOI: https://doi.org/10.1007/s40879-018-0296-z

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