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math.AG2020
Cascades of toric log del Pezzo surfaces of Picard number one
DongSeon Hwang
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 sho…
math.AG2020
On Barycentric transformations of Fano polytopes
DongSeon Hwang, Yeonsu Kim
We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the e…
math.AG2020
Symmetric and Kähler--Einstein Fano polygons
DongSeon Hwang, Yeonsu Kim
We investigate \emph{singular} symmetric and Kähler--Einstein Fano polytopes. More precisely, we show that every symmetric Fano polytope is Kähler--Einstein generalizing the work b…