K^2 = 6的燃烧曲面上的对数正则阈值

Pub Date : 2022-01-01 DOI:10.11650/tjm/220605

In-kyun Kim, Y. Shin

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引用次数: 0

摘要

．设S为一个Burniat曲面，其中K 2 S = 6， φ为S的双标准映射。本文通过Klein群G，给出了由φ诱导的S的多正则次线性系统的对数正则阈值的最优下界。实际上，对于正偶数m，一个不变量(正则表达式)的成员的对数正则阈值。逆不变)部分| mK S |大于或等于1 / (2 m)(相对于。1 / (2 m−2))。对于正奇数m，不变量(正则表达式)的成员的对数正则阈值。逆不变)部分| mK S |大于等于1 / (2 m−5)(p < 0.05)。1 / (2m))。不等式都是最优的。

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Log Canonical Thresholds on Burniat Surfaces with $K^2 = 6$ via Pluricanonical Divisors

. Let S be a Burniat surface with K 2 S = 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 | mK S | is greater than or equal to 1 / (2 m ) (resp. 1 / (2 m − 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 / (2 m − 5) (resp. 1 / (2 m )). The inequalities are all optimal.

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