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Cascades of toric log del Pezzo surfaces of Picard number one

황동선
대한수학회 (The Korean Mathematical Society)|2024.09|대한수학회지 (Journal of the KMS)|제61권 제5호|pp. 837-851|DOI 10.4134/JKMS.j210097

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참고문헌

키워드

Toric log del Pezzo surface$\mathbb{P}^1$-fibrationcascade
주제분류수학

초록

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 K\"ahler--Einstein metric, then it should admit a special cascade and it satisfies the equality of the orbifold Bogomolov--Miyaoka--Yau inequality, i.e., $K^2 = 3e_{orb}.$ Moreover, we provide an algorithm to compute a toric log del Pezzo surfaces of Picard number one for a given input of singularity types.

Abstract

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 K\"ahler--Einstein metric, then it should admit a special cascade and it satisfies the equality of the orbifold Bogomolov--Miyaoka--Yau inequality, i.e., $K^2 = 3e_{orb}.$ Moreover, we provide an algorithm to compute a toric log del Pezzo surfaces of Picard number one for a given input of singularity types.

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