Moduli space of J-holomorphic subvarieties
Moduli space of J-holomorphic subvarieties
复制标题
DOI：
10.1007/s00029-021-00648-z
复制
发表时间：
2016-01
期刊：
影响因子：
--
通讯作者：
Weiyi Zhang
中科院分区：
文献类型：
--
作者：
Weiyi Zhang
本文研究了四维辛流形中J-全纯子簇的模空间。对于任意驯服的几乎复杂的结构，我们表明，一个球类的模空间是由一个家庭的线性系统结构在代数几何。在这些应用中，我们给出了J-全纯子簇的各种唯一性结果，例如，对于无理直纹曲面中的纤维类和例外类。另一方面，探讨了复有理曲面中子簇的非唯一性和其它奇异现象。特别是，构造了具有更高属成分的例外类中的连通子变种。还讨论了环面的模空间，从而推广了椭圆曲线理论。
We study the moduli space ofJ-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 ofJ-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.