Resolution of singularities of toric orbifolds and equivariant cobordism of contact toric manifolds

TL;DR

This paper demonstrates how to resolve singularities in toric orbifolds and explores the equivariant cobordism properties of contact toric manifolds, establishing new connections between these geometric structures.

Contribution

It provides a method for resolving singularities of toric orbifolds and proves that certain contact toric manifolds are equivariantly boundaries, extending previous understanding.

Findings

Resolution of singularities for toric orbifolds established

Quasi-contact toric manifolds are shown to be equivariantly boundaries

Good contact toric manifolds and generalized lens spaces are boundaries

Abstract

Toric orbifolds are a generalization of simplicial projective toric varieties. In this paper, we show that there is a resolution of singularities of a toric orbifold. In a different category, the class of quasi-contact toric manifolds contains the class of good contact toric manifolds. We prove that a quasi-contact toric manifold is equivariantly a boundary. Moreover, we conclude that good contact toric manifolds and generalized lens spaces are equivariantly boundaries.