Lines on contact Manifolds IIb
| dc.creator | Kebekus, Stefan | |
| dc.date | 2003-06-17 | |
| dc.date | 2003-11-12 | |
| dc.date.accessioned | 2026-07-07T04:59:01Z | |
| dc.date.available | 2026-07-07T04:59:01Z | |
| dc.description | Let X be a complex-projective contact manifold whose second Betti-number is one. It has long been conjectured that X should then be rational-homogeneous, or equivalently, that there exists an embedding of X into a projective space whose image contains lines. Using methods introduced in math.AG/0206193, we show that X is covered by a compact family of rational curves, called "contact lines" that behave very much like the lines on the rational homogeneous examples: if x in X is a general point, then all contact lines through x are smooth, no two of them share a common tangent direction at x, and the union of all contact lines through x forms a cone over an irreducible, smooth base. As a corollary, we obtain that the tangent bundle of X is stable. | |
| dc.description | Fixed a number of minor issues found by the referee. To appear in Compositio Math. A PDF-file with additional graphics is available on the internet at http://www.mi.uni-koeln.de/~kebekus/publications-e.html | |
| dc.identifier | https://arxiv.org/abs/math/0306260 | |
| dc.identifier | http://arxiv.org/abs/math/0306260 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67814 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Lines on contact Manifolds IIb | |
| dc.type | text |