论文标题
汉密尔顿$ s^1 $ - actions of totlesstections
Hamiltonian $S^1$-actions on complete intersections
论文作者
论文摘要
我们研究了确定Kähler歧管哪种差异类别的问题，该类别允许汉密尔顿圆圈动作。我们的主要结果是以下结果：让$ m $成为封闭的符号歧管，与复杂尺寸$ 4K $的完整交点不同，具有Hamiltonian Circle Action，使固定点集的每个组件都是孤立的固定点或具有尺寸$ 2 \ mod 4 $。然后，$ m $是差异到$ \ mathbb {cp}^{4K} $，一个四边形$ q \ subset \ subset \ mathbb {cp}^{4K+1} $或两个Quadrics $ Q_1 \ c_1 \ cap q_2 \ cap q_2 \ subset \ subset \ subset \ mathbb} $ 2
We study the problem of determining which diffeomorphism classes of Kähler manifolds admit a Hamiltonian circle action. Our main result is the following: Let $M$ be a closed symplectic manifold, diffeomorphic to a complete intersection with complex dimension $4k$, having a Hamiltonian circle action such that each component of the fixed point set is an isolated fixed point or has dimension $2 \mod 4$. Then $M$ is diffeomorphic to $\mathbb{CP}^{4k}$, a quadric $Q \subset \mathbb{CP}^{4k+1}$ or an intersection of two quadrics $Q_1 \cap Q_2 \subset \mathbb{CP}^{4k+2}$.
