2001/02/01 by Jean-Claude Sikorav, Sikorav, Jean-Claude · 2 citations
Mathematics · #30G20 #53C65 #58F05 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.CV #math.SG #msc:30G20 #msc:53C65 #msc:58F05
paper · pdf · doi:10.48550/arxiv.math/0102004
24 pages. This paper is, apart for very minor corrections, unchanged from the ENS Lyon preprint of March 2000. Since its appearance, V. Shevchishin made much progress on the symplectic isotopy problem (cf. math.SG/0010262)
arxiv created 2001/02/01 · openalex publication_date 2001/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Under an assumption of normal genericity, we show that a stable J-holomorphic curve has, in the space of homologous curves of the same genus, a locally Euclidean neighbourhood of the expected dimension given by Riemann-Roch. In dimension 4, the normal genericity condition is satisfied in by every curve in CP2 (for an almost complex structure homotopic with the standard one) which has only nodes as singularities. This leads in particular to a solution of the symplectic isotopy problem for surfaces of degree 3.