Tropicalization of toric prevarieties
Alex K\"uronya, Pedro Souza, Martin Ulirsch

TL;DR
This paper develops a tropicalization procedure for toric prevarieties, extending existing tropical limit theorems to a broader class of algebraic structures, facilitating their study in tropical geometry.
Contribution
It introduces a tropicalization framework for toric prevarieties and generalizes key tropical limit theorems to divisorial schemes.
Findings
Established a tropicalization procedure for toric prevarieties.
Proved a generalized tropical limit theorem for divisorial schemes.
Enhanced understanding of tropical geometry for non-separated toric structures.
Abstract
The homogeneous spectrum of a multigraded finitely generated algebra (in the sense of Brenner-Schr\"oer) always admits an embedding into a toric variety that is not necessarily separated, a so-called toric prevariety. In order to have a convenient framework to study the tropicalization of homogeneous spectra we propose a tropicalization procedure for toric prevarieties and study its basic properties. With these tools at hand, we prove a generalization of Payne's and Foster--Gross--Payne's tropical limit theorem for divisorial schemes.
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