Nonrationality Degree of Toric Quasifolds

Toric quasifolds are nonrational generalizations of toric manifolds and orbifolds. We introduce the notion of nonrationality degree, an invariant that measures the extent to which a toric quasifold fails to be Hausdorff. We do so by first defining analogous notions for the underlying quasilattice and the corresponding quasitorus. We conclude by applying the nonrationality degree to reframe Gordan’s lemma in the nonrational setting.