论文标题
HOPF歧管上的购物中心束和平坦的连接
Mall bundles and flat connections on Hopf manifolds
论文作者
论文摘要
HOPF歧管H上的购物中心捆绑包是一个全态矢量捆绑包，其回调为H的通用封面是微不足道的。我们定义了共鸣和非谐振的购物中心束，概括了ODE中的共振概念，并证明非谐振的购物中心束总是承认平坦的全态连接。我们使用此观察结果证明了Poincare-Dulac线性化定理的一种版本，表明复杂空间的任何非共抗可逆性全态收缩在适当的全体形态坐标中都是线性的。我们定义了Hopf流形中共振的概念，并表明所有非共鸣的Hopf歧管都是线性的。以前，该结果是通过使用Poincare-Dulac定理获得的。
A Mall bundle on a Hopf manifold H is a holomorphic vector bundle whose pullback to the universal cover of H is trivial. We define resonant and non-resonant Mall bundles, generalizing the notion of the resonance in ODE, and prove that a non-resonant Mall bundle always admits a flat holomorphic connection. We use this observation to prove a version of Poincare-Dulac linearization theorem, showing that any non-resonant invertible holomorphic contraction of a complex space is linear in appropriate holomorphic coordinates. We define the notion of resonance in Hopf manifolds, and show that all non-resonant Hopf manifolds are linear; previously, this result was obtained by Kodaira using the Poincare-Dulac theorem.
