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

Abstract

. 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.