Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CASCADES OF TORIC LOG DEL PEZZO SURFACES OF PICARD NUMBER ONE

  • DongSeon Hwang (Center for Complex Geometry Institute for Basic Science (IBS))
  • Received : 2021.02.04
  • Accepted : 2024.04.26
  • Published : 2024.09.01
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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 admits a Kähler-Einstein metric, then it should admit a special cascade and it satisfies the equality of the orbifold Bogomolov-Miyaoka-Yau inequality, i.e., K2 = 3eorb. Moreover, we provide an algorithm to compute a toric log del Pezzo surfaces of Picard number one for a given input of singularity types.

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Acknowledgement

The author would like to express his deep gratitude to the referee for the careful reading and suggestions to improve the exposition of this paper. The author was supported by Samsung Science and Technology Foundation under Project SSTF-BA1602-03, the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2021R1A2C1093787), and the Institute for Basic Science (IBS-R032-D1).

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