CONTACT MANIFOLDS
Complex Projective Contact Manifolds
| Coordinatore | UNIVERSITE JOSEPH FOURIER GRENOBLE 1
Organization address
address: "Avenue Centrale, Domaine Universitaire 621" contact info |
| Nazionalità Coordinatore | France [FR] |
| Totale costo | 239˙138 € |
| EC contributo | 239˙138 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2007-4-1-IOF |
| Funding Scheme | MC-IOF |
| Anno di inizio | 2008 |
| Periodo (anno-mese-giorno) | 2008-09-01 - 2012-02-14 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITE JOSEPH FOURIER GRENOBLE 1
Organization address
address: "Avenue Centrale, Domaine Universitaire 621" contact info |
FR (GRENOBLE) | coordinator | 0.00 |
Mappa
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Obiettivo del progetto (Objective)
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.
Introduzione (Teaser)
The concept of manifolds in geometry and mathematical physics is key to studying complicated structures in terms of the well-understood properties of simpler spaces. Fano varieties are quite rare due to their projective spaces constituting closed algebraic sets.