Vol. 3, No. 6, 2009

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Effectiveness of the log Iitaka fibration for 3-folds and 4-folds

Gueorgui Todorov and Chenyang Xu

Vol. 3 (2009), No. 6, 697–710

We prove the effectiveness of the log Iitaka fibration in Kodaira codimension two for varieties of dimension 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.

Iitaka fibration, boundedness
Mathematical Subject Classification 2000
Primary: 14E05
Secondary: 14J35, 14J30
Received: 20 January 2009
Revised: 9 July 2009
Accepted: 17 August 2009
Published: 20 November 2009
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