Boundedness of the space of stable logarithmic maps

Abstract

We prove that the moduli space of stable logarithmic maps with fixed numerical invariants, from logarithmic curves to a fixed projective target logarithmic scheme with fine and saturated logarithmic structure, is a proper algebraic stack. This was previously known only with further restrictions on the logarithmic structure of the target.

32 pages, 2 figures. v3: Significant changes. Final version appears in the Journal of the European Mathematical Society

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