Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Semicascades of toric log del Pezzo surfaces

DongSeon Hwang

Ajou University

Abstract

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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