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Article Dans Une Revue Geometric And Functional Analysis Année : 2006

Towards relative invariants of real symplectic 4-manifolds

Résumé

Let $(X, \omega, c_X)$ 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 $(X, \omega, c_X, L)$ 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.
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Dates et versions

hal-04289661 , version 1 (16-11-2023)

Identifiants

Citer

Jean-Yves Welschinger. Towards relative invariants of real symplectic 4-manifolds. Geometric And Functional Analysis, 2006, 16 (5), pp.1157-1182. ⟨10.1007/s00039-006-0576-5⟩. ⟨hal-04289661⟩

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