Almost complex structure, blowdowns and McKay correspondence in quasitoric orbifolds

TL;DR

This paper establishes the existence of invariant almost complex structures on quasitoric orbifolds, constructs blowdowns, and explores a new McKay correspondence for non-Gorenstein orbifold toric varieties, including cohomological invariance results.

Contribution

It introduces a new McKay correspondence framework for non-Gorenstein orbifold toric varieties and constructs invariant almost complex structures and blowdowns.

Findings

Invariant almost complex structures exist on positively omnioriented quasitoric orbifolds.

Euler characteristic of Chen-Ruan cohomology is preserved under crepant blowdowns.

Betti numbers are preserved in dimensions up to six.

Abstract

We prove the existence of invariant almost complex structure on any positively omnioriented quasitoric orbifold. We construct blowdowns. We define Chen-Ruan cohomology ring for any omnioriented quasitoric orbifold. We prove that the Euler characteristic of this cohomology is preserved by a crepant blowdown. We prove that the Betti numbers are also preserved if dimension is less or equal to six. In particular, our work reveals a new form of McKay correspondence for orbifold toric varieties that are not Gorenstein. We illustrate with an example.