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Describing toric varieties and their equivariant cohomology

Matthias Franz — 2010

Colloquium Mathematicae

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...

Weights in cohomology and the Eilenberg-Moore spectral sequence

Matthias Franz; Andrzej Weber — 2005

Annales de l’institut Fourier

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 $G$ -variety $X$ ( $G$ being a connected algebraic group) in terms of its equivariant cohomology provided that $H_{G}^{*} (X)$ is pure. This is the case, for example, if $X$ is smooth and has only finitely many orbits. We work in the category...

Koszul duality and equivariant cohomology.

Franz, Matthias — 2006

Documenta Mathematica

Moment polytopes of projective $G$ -varieties and tensor products of symmetric group representations.

Franz, Matthias — 2002

Journal of Lie Theory

The classification of weighted projective spaces

Anthony Bahri; Matthias Franz; Dietrich Notbohm; Nigel Ray — 2013

Fundamenta Mathematicae

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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Currently displaying 1 – 5 of 5

Describing toric varieties and their equivariant cohomology

Weights in cohomology and the Eilenberg-Moore spectral sequence

Koszul duality and equivariant cohomology.

Moment polytopes of projective $G$ -varieties and tensor products of symmetric group representations.

The classification of weighted projective spaces

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

Describing toric varieties and their equivariant cohomology

Weights in cohomology and the Eilenberg-Moore spectral sequence

Koszul duality and equivariant cohomology.

Moment polytopes of projective G -varieties and tensor products of symmetric group representations.

The classification of weighted projective spaces

Moment polytopes of projective $G$ -varieties and tensor products of symmetric group representations.