Moduli of morphisms of logarithmic schemes

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.

45 pages; one error corrected, some new material on Zariski logarithmic structures, and a new appendix by Sam Molcho with explicit constructions in important examples; comments welcome!

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