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The fundamental group of a log terminal \(\mathbb{T}\)-variety. (English) Zbl 1425.14041

Summary: 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.

MSC:

14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14C15 (Equivariant) Chow groups and rings; motives
14C20 Divisors, linear systems, invertible sheaves
14E30 Minimal model program (Mori theory, extremal rays)
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