Submanifolds with corners in Delzant polytopes associated to affine subspaces

Abstract

We studied the closure of a complex subtorus given from an affine subspace in $\mathfrak{t}^{n} \cong \mathbb{R}^{n}$ 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.