The minimal model theorem for divisors of toric varieties

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概要

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• he minimal model conjecture says that if a proper variety has non-negative Kodaira dimension, then it has a minimal model with abundance and if the Kodaira dimension is -∞, then it is birationally equivalent to a variety which has a fibration with the relatively ample anti-canonical divisor. In this paper, first we prove this conjecture for a \varDelta-regular divisor on a proper toric variety by means of successive contractions of extremal rays and flips of the ambient toric variety. Then we prove the main result: for such a divisor with the non-negative Kodaira dimension there is an algorithm to construct concretely a projective minimal model with abundance by means of ``puffing up" the polytope.

• 東北大学の論文

著者

• Ishii Shihoko

  Department Of Mathematics Tokyo Institute Of Technology

関連論文

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• Divisorial Valuations via Arcs
• The minimal model theorem for divisors of toric varieties

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