#### Vol. 3, No. 6, 2009

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Effectiveness of the log Iitaka fibration for 3-folds and 4-folds

### Gueorgui Todorov and Chenyang Xu

Vol. 3 (2009), No. 6, 697–710
##### Abstract

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.

##### Keywords
Iitaka fibration, boundedness
##### Mathematical Subject Classification 2000
Primary: 14E05
Secondary: 14J35, 14J30
##### Milestones
Received: 20 January 2009
Revised: 9 July 2009
Accepted: 17 August 2009
Published: 20 November 2009
##### Authors
 Gueorgui Todorov Department of Mathematics Princeton University Princeton, NJ 08544 United States Chenyang Xu Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 United States