Minimal resolutions of toric substacks by line bundles

We construct minimal resolutions of pushforwards of structure sheaves of toric substacks of smooth toric stacks by line bundles as strong deformation retracts of cellular resolutions constructed by Hanlon, Hicks and Lazarev. We also provide a canonical and combinatorial description of the differentials of such minimal resolutions. Two key ingredients are the homological perturbation lemma and the Moore-Penrose inverses.