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We study a useful numerical invariant of normal surface singular-ities, introduced recently by T. Kawachi. Using this invariant, we give a quick proof of the (well-known) fact that all log-canonical surface singularities are either elliptic Gorenstein or rational (without assuming a priori that they are Q-Gorenstein). In §2 we prove effective results… (More)
Let M be a Q-divisor on a smooth surface over C. In this paper we give criteria for very ampleness of the adjoint of ⌈M ⌉, the roundup of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of Fujita's Conjecture in dimension 3.) In §4 we discuss an example which suggests that this kind of criteria might also… (More)