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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Published in:arXiv.org 2020-12
Main Author: Hwang, DongSeon
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Cascades
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description 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., \(K^2 = 3e_{orb}.\)
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title Cascades of toric log del Pezzo surfaces of Picard number one
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