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Complex Projective Contact Manifolds

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.

Call for proposal

FP7-PEOPLE-2007-4-1-IOF
See other projects for this call

Funding Scheme

MC-IOF - International Outgoing Fellowships (IOF)

Coordinator

UNIVERSITE JOSEPH FOURIER GRENOBLE 1
Address
Avenue Centrale, Domaine Universitaire 621
38041 Grenoble
France
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 239 138,19
Administrative Contact
Laurent Manivel (Prof.)