Submanifolds with corners in Delzant polytopes associated to affine subspaces

2024/02/20 by Yamaguchi, Kentaro
#14M25 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C40 #Secondary 53D20 #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2402.16884

Abstract

We studied the closure of a complex subtorus given from an affine subspace in \mathfraktⁿ ≅ ℝⁿ in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then we call such submanifold a torus-equivariantly embedded toric manifold with respect to the subtorus action determined by the data of the affine subspace. In this paper, we construct certain submanifolds with corners in a Delzant polytope of the toric manifold from the affine subspaces and show that the conditions for such submanifolds with corners are equivalent to those for torus-equivariantly embedded toric manifolds.

Related

• Torus-equivariantly embedded toric manifolds associated to affine subspaces
• Delzant type theorem for torus-equivariantly embedded toric hypersurfaces
• Two-dimensional equivariant symplectic submanifolds in toric manifolds
• Moduli spaces of Delzant polytopes and symplectic toric manifolds
• The main component of the toric Hilbert scheme