On complete intersections with trivial canonical class
  We prove birational boundedness results on complete intersections with trivial canonical class of base point free divisors in (some version of) Fano varieties. Our results imply in particular that Batyrev-Borisov toric construction produces only a bounded set of Hodge numbers in any given dimension, even as the codimension is allowed to grow. 
Lev A. Borisov, Zhan Li
math.AG