Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle   less than 2 \pi
  This is the second of a series of three papers which provide proofs of results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle is less than 2\pi. We show that these are in a natrual way projective algebraic varieties. In the case when the limiting variety and the limiting divisor are smooth we show that the limiting metric also has standard cone singularities. 
Xiuxiong Chen, Simon Donaldson, and Song Sun
math.DG math-ph math.AG math.MP