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A MEMO ON “INTRODUCTION TO THE TORIC MORI THEORY”BY OSAMU FUJINO AND HIROSHI

SATO

OSAMU FUJINO

This is a memorandum for ourselves.

(1) In Introduction, we supported [Ma, Remark 14-2-7]. However, the example in [Ma, Remark 14-2-7 (ii)] is not correct. The original statement in [KMM] is true. For the details, see the first author’s note: Classification of three-dimensional terminal toric flips. The latter part of the statement of [Ma, Corollary 14-2-2] contains a small gap.

(2) The last line in the proof of Theorem 4.1 is misleading. The strong convexity ofN E(X/Y) is obvious by the existence of an f-ample line bundle. It is independent of Kleiman’s criterion.

(3) In the statement of Proposition 4.6, there is a typo. ϕ is not projective but proper.

(4) In the statement of Theorem 6.5, there is a typo. A minimal modelshould be replaced by a dlt model.

Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602 Japan

E-mail address: [email protected]

Date: 2005/10/11.

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