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Abstract: The theory of momentum-angle complexes relies upon a construction that assigns to each
simplicial complex on the set {1,2,...,m} a space acted on by the m-dimensional torus and endowed with a special
bigraded cellular decomposition. In the framework of this construction the well-known nonsingular toric varieties
arise as orbit space of maximal free action of subtori on the momentum-angle complexes corresponding to simplicial spheres.
Different combinatorial invariants of simplicial complexes and well-known related combinatorial-geometrical objects
acquire a nice and surprisingly regular interpretation in terms of bigraded cohomology rings of the corresponding
momentum-angle complexes.
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