On Effective log Iitaka Fibration for 3-folds and 4-folds
  We prove the effectiveness of the log Iitaka fibration in Kodaira codimension two for varieties of dimension$\le 4$. In particular, we finish the proof of effective log Iitaka fibration in dimension two. Also, we show that for the log Iitaka fibration, if the fiber is of dimension two, the denominator of the moduli part is bounded. 
Gueorgui Todorov and Chenyang Xu