The L^2 dbar method, weak Lefschetz theorems, and the topology of Kahler manifolds
| dc.creator | Napier, T. | |
| dc.creator | Ramachandran, M. | |
| dc.date | 1997-12-29 | |
| dc.date.accessioned | 2026-07-07T01:51:26Z | |
| dc.date.available | 2026-07-07T01:51:26Z | |
| dc.description | A new approach to Nori's weak Lefschetz theorem is described. The new approach, which involves the dbar-method, avoids moving arguments and gives much stronger results. In particular, it is proved that if X and Y are connected smooth projective varieties of positive dimension and f is a holomorphic immersion of Y into X with ample normal bundle, then the image of the fundamental group of Y in that of X is of finite index. This result is obtained as a consequence of a direct generalization of Nori's theorem. The second part concerns a new approach to the theorem of Burns which states that a quotient of the unit ball in complex Euclidean space (of dimension at least 3) by a discrete group of automorphisms which has a strongly pseudoconvex boundary component has only finitely many ends. The following generalization is obtained. If a complete Hermitian manifold X of dimension at least 3 has a strongly pseudoconvex end E and the Ricci curvature of X is bounded above by a negative constant, then, away from E, X has finite volume. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9712030 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9712030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/301 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14E20 | |
| dc.title | The L^2 dbar method, weak Lefschetz theorems, and the topology of Kahler manifolds | |
| dc.type | text |