Taiwanese Journal of Mathematics

A Note on Iitaka's Conjecture $C_{3,1}$ in Positive Characteristics

Lei Zhang

Full-text: Open access

Abstract

Let $f \colon X \to Y$ be a fibration from a smooth projective $3$-fold to a smooth projective curve, over an algebraically closed field $k$ of characteristic $p \gt 5$. We prove that if the generic fiber $X_{\eta}$ has big canonical divisor $K_{X_{\eta}}$, then\[  \kappa(X)  \geq \kappa(Y) + \kappa(X_{\eta}).\]

Article information

Source
Taiwanese J. Math., Volume 21, Number 3 (2017), 689-704.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874614

Digital Object Identifier
doi:10.11650/tjm/7931

Mathematical Reviews number (MathSciNet)
MR3661388

Zentralblatt MATH identifier
06871339

Subjects
Primary: 14E05: Rational and birational maps 14E30: Minimal model program (Mori theory, extremal rays)

Keywords
Kodaira dimension positive characteristics weak positivity minimal model

Citation

Zhang, Lei. A Note on Iitaka's Conjecture $C_{3,1}$ in Positive Characteristics. Taiwanese J. Math. 21 (2017), no. 3, 689--704. doi:10.11650/tjm/7931. https://projecteuclid.org/euclid.twjm/1498874614


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