CORDIS
EU research results

CORDIS

English EN
Integral homology of toric varieties

Integral homology of toric varieties

Objective

The filtration of a toric variety by equivariant skeletal leads to a spectral sequence converging to the variety's Borel-Moore homology. Its E^1term is the direct sum of exterior algebras associated to the cones contained in the fan defining the toric variety. For rational coefficients this spectral sequence degenerates on the E^2 level. I conjecture that this holds true also over the integers and that there is no composition problem, i. eo, that one can compute the integral Borel-Moore homology of a toric variety from an explicitly known complex. This conjecture is supported by numerous examples. If true, it would be the first method to effectively compute the integral homology of singular toric varieties. The project is related to various topics at the borderline between topology and geometry, in particular to the homology and cohomology of algebraic varieties and their Chow groups. For instance, my conjecture would imply that the canonical map from Chow groups to Borel- Moore homology is injective for all toric varieties. Equivariant cohomology and equivariant Chow groups give additional information and will therefore be considered as well. Here Koszul duality comes in as an important algebraic tool to translate between ordinary and equivariant objects.

Leaflet | Map data © OpenStreetMap contributors, Credit: EC-GISCO, © EuroGeographics for the administrative boundaries

Coordinator

UNIVERSITE JOSEPH FOURIER - GRENOBLE 1

Address

Rue Des MathÉMatiques 100
38402 Saint-Martin-D'Heres

France

Administrative Contact

Claude FEUERSTEIN (Professor)

Project information

Grant agreement ID: HPMF-CT-2002-01566

  • Start date

    1 May 2002

  • End date

    30 April 2003

Funded under:

FP5-HUMAN POTENTIAL

  • Overall budget:

    € 59 550

  • EU contribution

    € 59 550

Coordinated by:

UNIVERSITE JOSEPH FOURIER - GRENOBLE 1

France