Objective The aim of this proposal is to investigate asymptotic invariants of linear systems on projective varieties, and their applications to polyhedral combinatorics. Beside cohomological invariants of such systems, we also intend to study notions coming from higher-dimensional geometry, which describe singularities of closed subschemes. Our research methods will include asymptotic invariants of linear systems, techniques from toric geometry and vanishing theorems for divisors.We plan to achieve our objectives via an intensive training and scientific cooperation with the Renyi Institute, which offers expertise in areas complementing mine. Parallel to the scientific mentoring process, a strong emphasis is put on furthering certain skills complementary to scientific research, such as research management and presentation skills. All along, a special care is taken for professional independence and leadership. Algebraic geometry is a modern are of mathematics on the leading edge of research. With its plentiful applications (among them Wiles' proof of the Fermat conjecture) and inter-disciplinary connections its further development can significantly increase the potential of European mathematics.Once achieved, our goals can have a strong fertilizing effect in several prestigious areas of mathematics, thus contribute to the competitiveness of the European Research Area. By connecting a world-renowned centre of algebraic geometry outside Europe, the project will effectively transfer state-of-the-art knowledge between various centres of excellence, to the advantage of European researchers. Fields of science natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Keywords birational classification of algebraic varieties higher higher-dimensional complex algebraic geometry linear systems polyhedral combinatorics rationality theorems singularity theory toric geometry Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Topic(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Call for proposal FP6-2004-MOBILITY-5 See other projects for this call Funding Scheme EIF - Marie Curie actions-Intra-European Fellowships Coordinator ALFRED RENYI INSTITUTE OF MATHEMATICS EU contribution No data Address Realtanoda u. 13-15 BUDAPEST Hungary See on map Links Website Opens in new window Total cost No data
