Abstract
Let $S$ be a Burniat surface with $K_S^2 = 6$ and $\varphi$ be the bicanonical map of $S$. In this paper we show optimal lower bounds of log canonical thresholds of members of pluricanonical sublinear systems of $S$ via Klein group $G$ induced by $\varphi$. Indeed, for a positive even integer $m$, the log canonical threshold of members of an invariant (resp. anti-invariant) part of $|mK_S|$ is greater than or equal to $1/(2m)$ (resp. $1/(2m-2)$). For a positive odd integer $m$, the log canonical threshold of members of an invariant (resp. anti-invariant) part of $|mK_S|$ is greater than or equal to $1/(2m-5)$ (resp. $1/(2m)$). The inequalities are all optimal.
Funding Statement
The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2020R1A2C4002510). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2020R1I1A1A01074847) and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A4A3033098).
Acknowledgments
The authors are very grateful to the referees for valuable suggestions and comments.
Citation
In-Kyun Kim. YongJoo Shin. "Log Canonical Thresholds on Burniat Surfaces with $K^2 = 6$ via Pluricanonical Divisors." Taiwanese J. Math. 26 (6) 1133 - 1144, December, 2022. https://doi.org/10.11650/tjm/220605
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