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On a conjecture of Shokurov: Characterization of toric varieties. (English) Zbl 1078.14515
Summary: We verify a special case of V. V. Shokurov’s conjecture [J. Math. Sci., New York 102, No. 2, 3876–3932 (2000; Zbl 1177.14078)] 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.

MSC:
14E30 Minimal model program (Mori theory, extremal rays)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
Citations:
Zbl 1177.14078
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