Boundedness of the space of stable logarithmic maps
  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. 
Dan Abramovich, Qile Chen, Steffen Marcus, Jonathan Wise
math.AG