Cascades of toric log del Pezzo surfaces of Picard number one

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 is K\"ahler-Einstein, then it should admit a special cascade, and it satisfies the equality of the orbifold Bogomolov-Miyaoka-Yau inequality, i.e....

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Bibliographic Details
Published in:arXiv.org 2020-12
Main Author: Hwang, DongSeon
Format: Article
Language:English
Subjects:
Cascades
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Summary: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 is K\"ahler-Einstein, then it should admit a special cascade, and it satisfies the equality of the orbifold Bogomolov-Miyaoka-Yau inequality, i.e., \(K^2 = 3e_{orb}.\)
ISSN:2331-8422