Objective
Research objectives and content
I plan to study compact hyperkahler manifolds by means of complex algebraic geometry. This comprises an investigation of the period map and other basic structures, eg. the ample cone, the Kahler cone, the cohomology ring, etc., naturally associated with such a manifold. The question will be approached by using the deformation theory and, more globally, the moduli space of hyperkahler manifolds.
A thourough analysis of some of the known higher-dimensional examples moduli spaces of bundles and Hilbert schemes of K3 surfaces) should clarify to what extent the theory of K3 surfaces generalizes to higher dimensions. Another interesting class of hyperkahler manifolds is provided by complex integrable systems. The study of these special structures promises to reveal important geometric properties of hyperkahler manifolds in general.
Last but not least, the underlying hyperkahler metric is encoded by the twistor space. I will attempt to give a concrete example of a twistor space and thus of a hyperkahler manifold. Note that explicit examples of hyperkahler metric on compact manifolds are extremely rare.
Training content (objective, benefit and expected impact)
The E. N. S. together with the many nearby institutions (eg., Jussieu, IHES) would provide an excellent training opportunity for algebraic geometers by offering specialized courses and seminars in several branches closely related to algebraic geometry,eg. differential and complex geometry, number theory.
The personal contact to leading experts (A. Beauville, M. Kontsevich, C Voisin) would be very inspiring and helpful for my own research work.
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 arithmetics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
You need to log in or register to use this function
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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.
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
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Data not available
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
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
75230 Paris
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.