Birational morphisms in quantum toric geometry

TL;DR

This paper explores birational morphisms in quantum toric geometry, focusing on weighted blow-ups and cobordism-induced morphisms between quantum toric stacks, extending classical concepts to stacks with irrational cones.

Contribution

It introduces the study of birational morphisms in quantum toric stacks, including weighted blow-ups with arbitrary weights and cobordism-induced morphisms, expanding classical toric geometry to the quantum setting.

Findings

Characterization of birational morphisms between quantum toric stacks.

Extension of weighted blow-ups to irrational cones.

Analysis of cobordism-induced morphisms in quantum toric geometry.

Abstract

In this paper, we investigate birational toric morphisms between quantum toric stacks -- namely, toric (analytic) stacks associated with fans whose cones may be irrational -- focusing on two primary classes of examples: weighted blow-ups with arbitrary weights, and morphisms induced by cobordisms.