Cascades of toric log del Pezzo surfaces of Picard number one

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 is Kähler-Einstein, then it should admit a special cascade, and it satisfies the equality of the orbifold Bogomolov-Miyaoka-Yau inequality, i.e., $K^2=3e_{orb}.$

References in corpus (1)

• Classification of toric log del Pezzo surfaces with few singular points