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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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From convex polytopes to toric varieties: the constructions of Davis and Januszkiewicz

In the definition of moment-angle manifold in Davis-Januszkiewicz's 1991 paper, the orbit space is a simple convex polytope $P$ which is contractible. We can replace $P$ by an arbitrary smooth nice ma …
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