Serre-Taubes duality for pseudoholomorphic curves
| dc.creator | Smith, Ivan | |
| dc.date | 2001-06-26 | |
| dc.date | 2001-07-13 | |
| dc.date.accessioned | 2026-07-07T04:42:19Z | |
| dc.date.available | 2026-07-07T04:42:19Z | |
| dc.description | According to Taubes, the Gromov invariants of a symplectic four-manifold X with b_+ > 1 satisfy the duality Gr(A) = +/- Gr(K-A), where K is Poincare dual to the canonical class. Extending joint work with Simon Donaldson in math.SG/0012067, we interpret this result in terms of Serre duality on the fibres of a Lefschetz pencil, by proving an analogous symmetry for invariants counting sections of associated bundles of symmetric products. Using similar methods we give a new proof of an existence theorem for symplectic surfaces in four-manifolds with b_+ = 1 and b_1 = 0. This reproves another theorem due to Taubes: two symplectic homology projective planes with negative canonical class and equal volume are symplectomorphic. | |
| dc.description | 52 pages, no figures; Section 5 has been re-written to include some additional motivation for the main conjecture (cf. Theorem 1.2) | |
| dc.identifier | https://arxiv.org/abs/math/0106220 | |
| dc.identifier | http://arxiv.org/abs/math/0106220 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61733 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53D35;57R17 | |
| dc.title | Serre-Taubes duality for pseudoholomorphic curves | |
| dc.type | text |