Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even...
We show that in the category of complex algebraic varieties, the Eilenberg–Moore
spectral sequence can be endowed with a weight filtration. This implies that it
degenerates if all spaces involved have pure cohomology. As application, we compute the
rational cohomology of an algebraic -variety ( being a connected algebraic
group) in terms of its equivariant cohomology provided that is pure. This is
the case, for example, if is smooth and has only finitely many orbits. We work in the
category...
We obtain two classifications of weighted projective spaces: up to hoeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid.
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