Tropical Toric Stacks Sample Clauses

Tropical Toric Stacks. ‌ The goal of this section is to give a tropical version of the work done in [GS15], namely to write down what a tropical toric stack is (at least when the ambi- ent space is T) and to describe the properties of maps between them. Before starting, consider the previous example of the stack [A2/µ2]. In terms of tropicalization we know what each of the pieces is individually, that Trop A2 = T2 and Trop µ2 is just a translation (with the condition that 2ζ = 0) with the action given by ζ · (x, y) '→ (x + ζ, y + ζ). It is also m a worth noting that this is a subgroup of Trop G2 (which is equal to G2 since multiplication becomes addition under tropicalization). Now that we know what each of the individual pieces are, and we know that they live in T2 we can take the stack quorient in the point-wise convergence topology. With this in mind we can make the following definition.
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