2008/10/09 by Eaman Eftekhary, Eftekhary, Eaman
Mathematics · #14N35 #53D45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14N35 #msc:53D45
paper · pdf · doi:10.48550/arxiv.0810.1640
This is a revision of the original submission. The assumption on the homology class is imposed in order to fill the gap in the original version
openalex publication_date 2008/10/09 · arxiv created 2012/10/02 · arxiv updated 2012/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a symplectic three-fold (M,ω) we show that for a generic almost complex structure J which is compatible with ω, there are finitely many J-holomorphic curves in M of any genus g≥ 0 representing a homology class β in \H2(M,\Z) with c1(M).β=0, provided that the divisibility of β is at most 4 (i.e. if β=nα with α∈ H2(M,\Z) and n∈ \Z then n≤ 4). Moreover, each such curve is embedded and 4-rigid.