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

Todorov, Gueorgui; Xu, Chenyang

doi:10.2140/ant.2009.3.697

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

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

Gueorgui Todorov and Chenyang Xu

Vol. 3 (2009), No. 6, 697–710

DOI: 10.2140/ant.2009.3.697

Abstract

We prove the effectiveness of the log Iitaka fibration in Kodaira codimension two for varieties of dimension $\leq 4$ . 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

Vol. 3, No. 6, 2009