• 대한수학회지
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• 제58권5호
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• pp.1081-1107
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• 2021

In this paper, we introduce the notion of toric special weak Fano manifolds, which have only special primitive crepant contractions. We study their structure, and in particular completely classify smooth toric special weak Fano 4-folds. As a result, we can confirm that almost every smooth toric special weak Fano 4-fold is a weakened Fano manifold, that is, a weak Fano manifold which can be deformed to a Fano manifold.