Blowdowns and McKay correspondence on four dimensional quasitoric orbifolds

TL;DR

This paper establishes the existence of torus invariant almost complex structures on four-dimensional primitive quasitoric orbifolds, constructs pseudo-holomorphic blowdowns, and proves a McKay correspondence version for crepant blowdowns.

Contribution

It introduces new methods for constructing almost complex structures and blowdowns on quasitoric orbifolds, extending McKay correspondence to this setting.

Findings

Existence of torus invariant almost complex structures on certain orbifolds

Construction of pseudo-holomorphic blowdowns

McKay correspondence for crepant blowdowns

Abstract

We prove the existence of torus invariant almost complex structure on any positively omnioriented four dimensional primitive quasitoric orbifold. We construct pseudo-holomorphic blowdown maps for such orbifolds. We prove a version of McKay correspondence when the blowdowns are crepant.