学术报告（文诗云10.8）

Equivariant Symplectic Submanifold of Toric Manifold

Equivariant Symplectic Submanifold of Toric Manifold

-

We study $2n$-dimensional symplectic toric manifolds, and give a description of a symplectic submanifold $N^{2n-2}$ carrying an effective subtorus $T^{n-1}$-action, by the  moment map $\mu$ of a toric manifold $(M^{2n},\omega,T^n,\mu)$. Its image $\mu\circ i(N^{2n-2})$ is a smooth hypersurface of $\Delta^n$ with some restrictions. And we prove that in some cases there exists a symplectic submanifold $N^{2n-2}$, carrying an effective subtorus $T^{n-1}$-action, such that the image $\mu\circ i(N^{2n-2})$ is a smooth hypersurface of $\Delta^n$.