Delzant type theorem for torus-equivariantly embedded toric hypersurfaces

TL;DR

This paper generalizes Delzant's theorem by providing conditions for nonsingularity of closures of codimension one complex subtorus orbits in symplectic toric manifolds, using polytope criteria.

Contribution

It extends Delzant's theorem to a broader class of toric hypersurfaces by characterizing nonsingularity via polytopal conditions.

Findings

Established a polytope-based criterion for nonsingularity of toric hypersurfaces.

Generalized Delzant's theorem to include codimension one subtorus orbit closures.

Abstract

In the previous work, we study the moment polytope of the closure of the complex subtorus orbit in a symplectic toric manifold associated to an affine subspace when the closure is a smooth complex submanifold. In this paper, we clarify the condition for nonsingularity of the closure of the codimension one complex subtorus orbit in terms of polytopes. The main result is a generalization of Delzant theorem.