Tohoku Mathematical Journal
2013
March
SECOND SERIES VOL. 65, NO. 1

Tohoku Math. J.
65 (2013), 93-103

Title ON THE ACC FOR LENGTHS OF EXTREMAL RAYS

Author Osamu Fujino and Yasuhiro Ishitsuka

(Received October 12, 2011)
Abstract. We discuss the ascending chain condition for lengths of extremal rays. We prove that the lengths of extremal rays of $n$-dimensional $\boldsymbol{Q}$-factorial toric Fano varieties with Picard number one satisfy the ascending chain condition.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 14E30.
Key words and phrases. Ascending chain condition, lengths of extremal rays, Fano varieties, toric varieties, minimal model program.

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