Objective
Let G be a reductive linear algebraic group over the complex numbers. A G-variety, an algebraic variety with an algebraic action of the group G, is said to be spherical if it is normal and has an open orbit for a maximal connected solvable subgroup of G. We aim to complete the classification of spherical varieties by proving Luna's conjecture on a special class of spherical varieties, called wonderful. To a wonderful variety one can naturally associate an invariant combinatorial object in terms of roots and weights, called spherical system. Luna's conjecture states that there exists a one-to-one correspondence between isomorphism classes of wonderful varieties and spherical systems. Given a spherical system, here we want to provide the corresponding wonderful variety by studying the geometric properties of a certain algebraic scheme, called invariant Hilbert scheme, recently introduced by Alexeev and Brion. The given reductive group G acts linearly on the ring of regular functions of any affine spherical G-variety, the corresponding linear representation is multiplicity-free. The invariant Hilbert scheme of Alexeev and Brion parameterises the affine spherical G-varieties with a fixed multiplicity-free representation in their ring of regular functions. It is endowed with an action of a maximal torus of the group G. Given a spherical system, the strategy is to define a suitable multiplicity-free representation and study the corresponding invariant Hilbert scheme. Via deformation theory arguments we want to prove that under certain conditions the considered invariant Hilbert scheme has an open orbit for the toric action. By a standard procedure, called spherical closure, one can associate to any spherical variety a wonderful variety. Here we want to prove that to an affine spherical variety corresponding to a generic point in the invariant Hilbert scheme it is associated a wonderful variety with the given spherical system.
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.
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Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2007-2-1-IEF
See other projects for this call
Funding Scheme
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.
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
38041 GRENOBLE
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.