GENERAL n-CANONICAL DIVISORS ON TWO-DIMENSIONAL SMOOTHABLE SEMI-LOG-TERMINAL SINGULARITIES
نویسنده
چکیده
This paper is devoted to some fundumental calculation on 2-dimensional smoothable semi-log-terminal singularities. If we study minimal or canonical models of one parameter degeneration of algebraic surfaces, we must treat singularities that appear in the central fiber. Smoothable semi-log-terminal singularities are the singularities of the central fiber of the minimal model of degeneration, and the singularities of the central fiber of the canonical model of degeneration which may have large Gorenstein index. Kollár and Shepherd-Barron caracterized these singularities in [K-SB], but for numerical theory of degeneration, we need more detailed information. In this paper, we calculate general n-canonical divisors on these singularities, in other words, we calculate the full sheaves associated to the double dual of the n-th tensor power of the dualizing sheaves. And the application of this result, we bound the Gorenstein index by the local self intersection number of the n-canonical divisor. Notation: In this paper,
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