TL;DR
Toric quasifolds are complex, highly singular spaces extending classical toric geometry to non-rational polytopes, with detailed examples and foundational considerations from a symplectic perspective.
Contribution
This paper introduces toric quasifolds, expanding toric geometry to non-rational polytopes, and provides illustrative examples and foundational insights.
Findings
Description of notable examples of toric quasifolds
Development of atlases for toric quasifolds
Discussion of foundational considerations in the theory
Abstract
Toric quasifolds are highly singular spaces that were first introduced in order to address, from the symplectic viewpoint, the longstanding open problem of extending the classical constructions of toric geometry to those simple convex polytopes that are not rational. We illustrate toric quasifolds, and their atlases, by describing some notable examples. We conclude with a number of considerations.
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