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On the \(\mathbb A^1\)-fundamental groups of smooth toric varieties. (English) Zbl 1276.14035
Summary: We provide combinatorial descriptions of \(\mathbb A^1\)-fundamental groups of smooth toric varieties. As a corollary, a smooth projective toric variety for which the irrelevant ideal in the Cox ring has codimension \(\geqslant 3\) has a torus as \(\mathbb A^1\)-fundamental group.

MSC:
14F42 Motivic cohomology; motivic homotopy theory
14F35 Homotopy theory and fundamental groups in algebraic geometry
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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