Tohoku Mathematical Journal
2007
December
SECOND SERIES VOL. 59, NO. 4

Tohoku Math. J.
59 (2007), 481-525

Title DOMINANT RATIONAL MAPS IN THE CATEGORY OF LOG SCHEMES

Author Isamu Iwanari and Atsushi Moriwaki

(Received May 9, 2005, revised June 25, 2007)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 14G05; Secondary 14E05.

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