• Title/Summary/Keyword: ${\mathbb{P}}^1$-fibration

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CASCADES OF TORIC LOG DEL PEZZO SURFACES OF PICARD NUMBER ONE

  • DongSeon Hwang
    • Journal of the Korean Mathematical Society
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    • v.61 no.5
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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 = 3eorb. Moreover, we provide an algorithm to compute a toric log del Pezzo surfaces of Picard number one for a given input of singularity types.

  • https://doi.org/10.4134/JKMS.j210097 인용 PDF