We study the moduli space of J-holomorphic subvarieties in a 4-dimensional symplectic manifold. For an arbitrary tamed almost complex structure, we show that the moduli space of a sphere class is formed by a family of linear system structures as in algebraic geometry. Among the applications, we show various uniqueness results of J-holomorphic subvarieties, e.g. for the fiber and exceptional classes in irrational ruled surfaces. On the other hand, non-uniqueness and other exotic phenomena of subvarieties in complex rational surfaces are explored. In particular, connected subvarieties in an exceptional class with higher genus components are constructed. The moduli space of tori is also discussed, and leads to an extension of the elliptic curve theory.

我们研究的模空间Ĵ在4维辛流-holomorphic子簇。对于任意驯服的几乎复杂的结构，我们表明球类的模空间是由一族线性系统结构形成的，如代数几何一样。在这些应用中，我们显示了J-亚纯亚型的各种唯一性结果，例如，对于非规则直纹曲面中的纤维和特殊类。另一方面，研究了复杂有理曲面中的子变量的非唯一性和其他奇异现象。特别地，构造具有较高属成分的例外类别中的连接亚变体。还讨论了圆托的模空间，并导致椭圆曲线理论的扩展。