Log Canonical Thresholds on Burniat Surfaces with 𝑲² = 6 via Pluricanonical Divisors

Let 𝑆 be a Burniat surface with K S 2 = 6 and φ 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 φ. Indeed, for a positive even integer m, the log canonical threshold o...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 26; no. 6; pp. 1133 - 1144
Main Authors Kim, In-Kyun, Shin, YongJoo
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2022
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Summary:Let 𝑆 be a Burniat surface with K S 2 = 6 and φ 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 φ. Indeed, for a positive even integer m, the log canonical threshold of members of an invariant (resp. anti-invariant) part of |m𝑲𝑆| 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 |m𝑲𝑆| is greater than or equal to 1/(2m – 5) (resp. 1/(2m)). The inequalities are all optimal.
ISSN:1027-5487
2224-6851