Lefschetz pencils and the canonical class for symplectic 4-manifolds
| dc.creator | Donaldson, Simon | |
| dc.creator | Smith, Ivan | |
| dc.date | 2000-12-10 | |
| dc.date | 2001-11-05 | |
| dc.date.accessioned | 2026-07-07T04:39:08Z | |
| dc.date.available | 2026-07-07T04:39:08Z | |
| dc.description | We present a new proof of a result due to Taubes: if X is a closed symplectic four-manifold with b_+(X) > 1+b_1(X) and with some positive multiple of the symplectic form a rational class, then the Poincare dual of the canonical class of X may be represented by an embedded symplectic submanifold. The result builds on the existence of Lefschetz pencils on symplectic four-manifolds. We approach the topological problem of constructing submanifolds with locally positive intersections via almost complex geometry. The crux of the argument is that a Gromov invariant counting pseudoholomorphic sections of an associated bundle of symmetric products is non-zero. | |
| dc.description | 47 pages. The role of the transversality argument in Section 7 has been clarified, and the treatments of smoothing nodal surfaces controlling bubbling have been revised. Various other minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0012067 | |
| dc.identifier | http://arxiv.org/abs/math/0012067 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60538 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53D05 | |
| dc.title | Lefschetz pencils and the canonical class for symplectic 4-manifolds | |
| dc.type | text |