Objectif In our project we are interested in the classification of complex projective contact Fano manifolds and of quaternion-Kahler manifolds with positive scalar curvature. Also we want to classify smooth subvarieties of projective space whose dual is also smooth. We divide these problems into the following four objectives: 1) to expand the dictionary between the differential geometric properties of quaternion-Kahler manifolds with positive scalar curvature and algebro-geometric properties of complex contact Fano manifolds; 2) to determine properties of minimal rational curves on contact Fano manifolds and the Legendrian subvarieties determined by these curves; 3) to use the results of 1) and 2) to make progress in establishing or disproving the conjecture of LeBrun and Salamon - we will approach the conjecture from both the differential and algebraic perspectives. 4) to classify smooth varieties whose dual is also smooth via Legendrian varieties. Mots‑clés Legendrian varieties algebraic geometry contact manifolds differential geometry quaternion-Kahler manifolds self-dual varieties smooth varieties with smooth dual Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) PEOPLE-2007-4-1.IOF - Marie Curie Action: "International Outgoing Fellowships for Career Development" Appel à propositions FP7-PEOPLE-2007-4-1-IOF Voir d’autres projets de cet appel Régime de financement MC-IOF - International Outgoing Fellowships (IOF) Coordinateur UNIVERSITE JOSEPH FOURIER GRENOBLE 1 Contribution de l’UE € 239 138,19 Adresse Avenue Centrale, Domaine Universitaire 621 38041 GRENOBLE France Voir sur la carte Type d’activité Higher or Secondary Education Establishments Contact administratif Laurent Manivel (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
