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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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##### References:
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