, Volume 146, Issue 1, pp 43-66
Date: 06 Nov 2009

Enriques diagrams and log-canonical thresholds of curves on smooth surfaces

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Abstract

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.

Marian Aprodu was supported in part by the PCE Grant PNII 2228 (502/2009). He expresses his thanks to the LAREMA Angers for hospitality during the preparation of this work.