Cascades of toric log del Pezzo surfaces of Picard number one
DongSeon Hwang
TL;DR
This paper classifies a special class of toric log del Pezzo surfaces with Picard number one using a new concept called cascades, and explores their geometric properties related to Kähler-Einstein metrics and inequalities.
Contribution
It introduces the notion of cascades to classify toric log del Pezzo surfaces of Picard number one and links this to their Kähler-Einstein property and Bogomolov-Miyaoka-Yau equality.
Findings
Surfaces admit special cascades if they are Kähler-Einstein.
Kähler-Einstein surfaces satisfy the orbifold Bogomolov-Miyaoka-Yau equality.
Classification via cascades provides new insights into the geometry of these surfaces.
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 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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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry