About a Minimal Model Program without flips
  We introduce a new vector space associated to projective variety, the Weil Neron-Severi space, which we show is finitely generated and contains the usual Neron-Severi space as a subspace. We define the Nef cone of Weil divisor and the cone of Weil curves. We study these cones, and prove a new Cone theorem. We use this theorem to propose a Minimal Model Program without flips. 
Alberto Chiecchio
math.AG