## Algebra & Number Theory

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

#### Abstract

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.

#### Article information

Source
Algebra Number Theory, Volume 3, Number 6 (2009), 697-710.

Dates
Revised: 9 July 2009
Accepted: 17 August 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513797470

Digital Object Identifier
doi:10.2140/ant.2009.3.697

Mathematical Reviews number (MathSciNet)
MR2579391

Zentralblatt MATH identifier
1184.14023

Subjects
Primary: 14E05: Rational and birational maps
Secondary: 14J35: $4$-folds 14J30: $3$-folds [See also 32Q25]

Keywords
Iitaka fibration boundedness

#### Citation

Todorov, Gueorgui; Xu, Chenyang. Effectiveness of the log Iitaka fibration for 3-folds and 4-folds. Algebra Number Theory 3 (2009), no. 6, 697--710. doi:10.2140/ant.2009.3.697. https://projecteuclid.org/euclid.ant/1513797470

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