JournalsjemsVol. 19, No. 9pp. 2783–2809

Boundedness of the space of stable logarithmic maps

  • Dan Abramovich

    Brown University, Providence, USA

  • Qile Chen

    Columbia University, New York, and Boston College, Chestnut Hill, USA

  • Steffen Marcus

    The College of New Jersey, Ewing, USA

  • Jonathan Wise

    University of Colorado, Boulder, USA
Boundedness of the space of stable logarithmic maps cover
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Abstract

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.

Cite this article

Dan Abramovich, Qile Chen, Steffen Marcus, Jonathan Wise, Boundedness of the space of stable logarithmic maps. J. Eur. Math. Soc. 19 (2017), no. 9, pp. 2783–2809

DOI 10.4171/JEMS/728