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In this paper we calculate genaral n-canonical divisors on smoothablesemi-log-terminal singularities in dimension 2, in other words, the fullsheaves associated to the double dual of the nth tensor power of the dualizingsheaves of these singularities. And as its application we give the inequalitywhich bound the Gorenstein index by the local self intersection number of then-canonical divisor of these singularities.

General multi-canonical divisors on two-dimensional smoothable semi-log-terminal singularities