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On $-K^2$ for normal surface singularities

Hao Chen·Shihoko Ishii
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Abstract

In this paper we show the lower bound of the set of non-zero $-K^2$ for normal surface singularities establishing that this set has no accumulation points from above. We also prove that every accumulation point from below is a rational number and every positive integer is an accumulation point. Every rational number can be an accumulation point modulo $\bZ$. We determine all accumulation points in $[0, 1]$. If we fix the value $-K^2$, then the values of $p_g$, $p_a$, mult, embdim and the numerical indices are bounded, while the numbers of the exceptional curves are not bounded.

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Hao Chen, Shihoko Ishii. 1998-03-12. On $-K^2$ for normal surface singularities. https://arxiv.org/abs/math/9803047

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