Tohoku Mathematical Journal

Dominant rational maps in the category of log schemes

Isamu Iwanari and Atsushi Moriwaki

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Kobayashi-Ochiai's theorem states that the set of dominant rational maps from a complex variety to a complex variety of general type is finite. Kazuya Kato conjectured a similar result in the category of log schemes. Our main theorem of this paper is a solution to his conjecture.

Article information

Tohoku Math. J. (2), Volume 59, Number 4 (2007), 481-525.

First available in Project Euclid: 6 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G05: Rational points
Secondary: 14E05: Rational and birational maps


Iwanari, Isamu; Moriwaki, Atsushi. Dominant rational maps in the category of log schemes. Tohoku Math. J. (2) 59 (2007), no. 4, 481--525. doi:10.2748/tmj/1199649872.

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