Towards relative invariants of real symplectic 4-manifolds
| dc.creator | Welschinger, Jean-Yves | |
| dc.date | 2005-02-16 | |
| dc.date.accessioned | 2026-07-07T05:17:05Z | |
| dc.date.available | 2026-07-07T05:17:05Z | |
| dc.description | Let $(X, ω, c_X)$ be a real symplectic 4-manifold with real part $R X$. Let $L \subset R X$ be a smooth curve such that $[L] = 0 \in H_1 (R X ; Z / 2Z)$. We construct invariants under deformation of the quadruple $(X, ω, c_X, L)$ by counting the number of real rational $J$-holomorphic curves which realize a given homology class $d$, pass through an appropriate number of points and are tangent to $L$. As an application, we prove a relation between the count of real rational $J$-holomorphic curves done in math.AG/0303145 and the count of reducible real rational curves done in math.SG/0502355. Finally, we show how these techniques also allow to extract an integer valued invariant from a classical problem of real enumerative geometry, namely about counting the number of real plane conics tangent to five given generic real conics. | |
| dc.description | 21 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0502358 | |
| dc.identifier | http://arxiv.org/abs/math/0502358 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74223 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53D45; 14N35; 14N10; 14P99 | |
| dc.title | Towards relative invariants of real symplectic 4-manifolds | |
| dc.type | text |