2023/06/27 by Kentaro Yamaguchi, Yamaguchi, Kentaro
Computer Science · Mathematics · #14M25 #53D20 #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Primary 53C40 #Secondary 53C55 #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2306.15312
openalex publication_date 2023/06/27 · openalex created_date 2023/06/29 · openalex updated_date 2026/07/28
We study the closure of a complex subtorus in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then the subtorus action on such submanifold is Hamiltonian. In this case, we may think of the embedding of the submanifold as torus-equivariant. We show that the image of the moment map for the Hamiltonian subtorus action on our submanifold coincides with the image of the Delzant polytope of the ambient toric manifold under the pullback of the inclusion of the tori. The submanifolds constructed in the present paper are called torus-equivariantly embedded toric manifolds with respect to the subtorus action.