Moduli of morphisms of logarithmic schemes

TL;DR

This paper establishes the existence of a logarithmic algebraic space that parametrizes morphisms between fixed logarithmic schemes under certain conditions, leading to new insights into the algebraicity of stacks of stable logarithmic maps.

Contribution

It introduces a new logarithmic algebraic space for morphisms and proves the algebraicity of the stack of stable logarithmic maps without restrictions.

Findings

Existence of a logarithmic algebraic space for morphisms

Algebraicity of the stack of stable logarithmic maps

No restrictions on the target's logarithmic structure

Abstract

We show that there is a logarithmic algebraic space parameterizing logarithmic morphisms between fixed logarithmic schemes when those logarithmic schemes satisfy natural hypotheses. As a corollary, we obtain the algebraicity of the stack of stable logarithmic maps without restriction on the logarithmic structure of the target.