On the fundamental group of real toric varieties
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LetX (Δ) be the real toric variety associated to a smooth fan Δ. The main purpose of this article is: (i) to determine the fundamental group and the universal cover ofX (Δ), (ii) to give necessary and sufficient conditions on Δ under which π1(X(Δ)) is abelian, (iii) to give necessary and sufficient conditions on Δ under whichX(Δ) is aspherical, and when Δ is complete, (iv) to give necessary and sufficient conditions forC Δ to be aK (π, 1) space whereC Δ is the complement of a real subspace arrangement associated to Δ.
KeywordsReal toric varieties fundamental group asphericity K (Π, 1) subspace arrangements
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