A characterization of the vanishing of the second plurigenus for normal surface singularities
Bull. Korean Math. Soc. 2008 Vol. 45, No. 2, 221-230
Printed June 1, 2008
Koukichi Wada
Tokyo University of Agriculture
Abstract : In the study of normal (complex analytic) surface singularities, it is interesting to investigate the invariants. The purpose of this paper is to give a characterization of the vanishing of $\delta_2$. In \cite{Wada}, we gave characterizations of minimally elliptic singularities and rational triple points in terms of the second plurigenera $\delta_2$ and $\gamma_2$. In this paper, we also give a characterization of rational triple points in terms of a certain computation sequence. To prove our main theorems, we give two formulae for $\delta_2$ and $\gamma_2$ of rational surface singularities.
Keywords : second plurigenus, rational surface singularity, rational triple points
MSC numbers : Primary 14J17; Secondary 32S12
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