Fano contact manifolds and nilpotent orbits
| dc.creator | Beauville, Arnaud | |
| dc.date | 1997-07-24 | |
| dc.date.accessioned | 2026-07-07T09:07:21Z | |
| dc.date.available | 2026-07-07T09:07:21Z | |
| dc.description | A contact structure on a complex manifold M is a corank 1 subbundle F of T(M) such that the bilinear form on F with values in the quotient line bundle L=T(M)/F deduced from the Lie bracket of vector fields is everywhere non-degenerate. In this paper we consider the case where M is a Fano manifold; this implies that L is ample. If g is a simple Lie algebra, the unique closed orbit in P(g) (for the adjoint action) is a Fano contact manifold; it is conjectured that every Fano contact manifold is obtained in this way. A positive answer would imply an analogous result for compact quaternion-Kahler manifolds with positive scalar curvature, a longstanding question in Riemannian geometry. In this paper we solve the conjecture under the additional assumptions that the group of contact automorphisms of M is reductive, and that the image of the rational map M - - -> P(H0(M,L)*) associated to L has maximum dimension. The proof relies on the properties of the nilpotent orbits in a semi-simple Lie algebra, in particular on the work of R. Brylinski and B. Kostant. | |
| dc.description | Plain TeX. Postscript file available at http://www..dmi.ens.fr/users/beauvill/ | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9707015 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9707015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150343 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Fano contact manifolds and nilpotent orbits | |
| dc.type | text |