Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry

• 成果类型: Article
• 署名作者: Welschinger, JY
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0445-0
• 发表日期: 2005
• 页码: 195-234
• 关键词: curves

摘要

We first build the moduli spaces of real rational pseudo-holomorphic curves in a given real symplectic 4-manifold. Then, following the approach of Gromov and Witten [3,19,11], we define invariants under deformation of real symplectic 4-manifolds. These invariants provide lower bounds for the number of real rational J-holomorphic curves which realize a given homology class and pass through a given real configuration of points.