• 대한수학회지
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• 제61권5호
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• pp.837-851
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• 2024

We classify toric log del Pezzo surfaces of Picard number one by introducing the notion, cascades. As an application, we show that if such a surface admits a Kähler-Einstein metric, then it should admit a special cascade and it satisfies the equality of the orbifold Bogomolov-Miyaoka-Yau inequality, i.e., K² = 3e_orb. Moreover, we provide an algorithm to compute a toric log del Pezzo surfaces of Picard number one for a given input of singularity types.