Enriques diagrams and log-canonical thresholds of curves on smooth surfaces
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- Aprodu, M. & Naie, D. Geom Dedicata (2010) 146: 43. doi:10.1007/s10711-009-9425-7
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It is shown that, on a smooth surface, the log-canonical threshold of a curve with an isolated singularity is computed by the term ideal of the curve in a suitable system of local parameters at the singularity. The proof uses the Enriques diagram of the singularity and shows that the log-canonical threshold depends only on a non-degenerate path of that diagram.