Moduli of surfaces with an anti-canonical cycle
  We prove a global Torelli theorem for pairs (Y,D), where Y is a smooth projective rational surface and D is an effective anti-canonical divisor which is a cycle of rational curves. This Torelli theorem was conjectured by Friedman in 1984. In addition, we construct natural universal families for such pairs. 
Mark Gross, Paul Hacking, Sean Keel
math.AG