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Boundedness of the space of stable logarithmic maps. (English) Zbl 06773013
Summary: We prove that the moduli space of stable logarithmic maps from logarithmic curves to a fixed target logarithmic scheme is a proper algebraic stack when the target scheme is projective with fine and saturated logarithmic structure. This was previously known only with further restrictions on the logarithmic structure of the target.

MSC:
14H10 Families, moduli of curves (algebraic)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14D23 Stacks and moduli problems
14A20 Generalizations (algebraic spaces, stacks)
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