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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics geometry
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
38402 SAINT-MARTIN-D'HERES
France
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