# Symmetric and Kähler-Einstein toric log del Pezzo surfaces

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DongSeon Hwang, Yeonsu Kim

We investigate symmetric and Kähler-Einstein toric log del Pezzo surfaces. It turns out that the property of being symmetric and Kähler-Einstein is determined by the torus-equivariant automorphism of the surface. In particular, we show, by exhibiting examples, that the class of Kähler-Einstein toric log del Pezzo surfaces and the class of symmetric toric log del Pezzo surfaces do not belong to each other. Moreover, we completely classify symmetric toric log del Pezzo surfaces that are not Kähler-Einstein.

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