Tohoku Mathematical Journal
2001
December
SECOND SERIES VOL. 53, NO. 4

Tohoku Math. J.
53 (2001), 581-892

Title ON A CONJECTURE OF SHOKUROV: CHARACTERIZATION OF TORIC VARIETIES

Author Yuri G. Prokhorov

(Received January 31, 2000)
Abstract. We verify a special case of V. V. Shokurov's conjecture about characterization of toric varieties. More precisely, we consider three-dimensional log varieties with only purely log terminal singularities and numerically trivial log canonical divisor. In this situation we prove an inequality connecting the rank of the group of Weil divisors modulo algebraic equivalence and the sum of coefficients of the boundary. We describe such varieties for which the equality holds and show that all of them are toric.

2000 Mathematics Subject Classification. Primary 14E30; Secondary 14M25, 14J17.

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