GIT Compactifications of M_{0,n} and Flips
  We use geometric invariant theory (GIT) to construct a large class of compactifications of the moduli space M_{0,n}. These compactifications include many previously known examples, as well as many new ones. As a consequence of our GIT approach, we exhibit explicit flips and divisorial contractions between these spaces. 
Noah Giansiracusa, David Jensen, and Han-Bom Moon
math.AG