Bull. Korean Math. Soc. 2022; 59(1): 179-190
Online first article June 17, 2021 Printed January 31, 2022
https://doi.org/10.4134/BKMS.b210211
Copyright © The Korean Mathematical Society.
DongSeon Hwang
Ajou University
A cascade of toric log del Pezzo surfaces of Picard number one was introduced as a language of classifying all such surfaces. In this paper, we introduce a generalized concept, a semicascade of toric log del Pezzo surfaces. As applications, we discuss K\"ahler--Einstein toric log del Pezzo surfaces and derive a bound on the Picard number in terms of the number of singular points, generalizing some results of Dais and Suyama.
Keywords: Toric log del Pezzo surface, toric graph, semicascade
MSC numbers: Primary 14M25; Secondary 14J45, 14J26, 52B20
Supported by: The author would like to thank Fei Xie and Edwin Kutas for useful discussions regarding the first version of the paper. This research was supported by Samsung Science and Technology Foundation under Project SSTF-BA1602-03.
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