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Describing toric varieties and their equivariant cohomology

100%

Franz M.

Colloquium Mathematicum

2010

tom 121

nr 1

1-16

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 degrees. This generalizes a result of Bahri-Franz-Ray to the non-compact case. We also investigate torsion phenomena in integral cohomology.

The classification of weighted projective spaces

51%

Bahri A., Franz M., Notbohm D., Ray N.

Fundamenta Mathematicae

2013

tom 220

nr 3

217-226

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Franz M.

1 Bahri A.

1 Notbohm D.

1 Ray N.

1 2013

1 2010

Wyniki wyszukiwania

Describing toric varieties and their equivariant cohomology

The classification of weighted projective spaces