CONTACT MANIFOLDS

Complex Projective Contact Manifolds

Coordinatore	UNIVERSITE JOSEPH FOURIER GRENOBLE 1    more  Organization address address: "Avenue Centrale, Domaine Universitaire 621" city: GRENOBLE postcode: 38041 contact info Titolo: Prof. Nome: Laurent Cognome: Manivel Email: send email Telefono: +33 4 76 51 49 03 Fax: +33 4 76 51 44 78
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

#	participant	country	role	EC contrib. [€]
1	UNIVERSITE JOSEPH FOURIER GRENOBLE 1  Organization address address: "Avenue Centrale, Domaine Universitaire 621" city: GRENOBLE postcode: 38041 contact info Titolo: Prof. Nome: Laurent Cognome: Manivel Email: send email Telefono: +33 4 76 51 49 03 Fax: +33 4 76 51 44 78	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.