Geometriae Dedicata

, Volume 146, Issue 1, pp 43–66

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

Original Paper

DOI: 10.1007/s10711-009-9425-7

Cite this article as:
Aprodu, M. & Naie, D. Geom Dedicata (2010) 146: 43. doi:10.1007/s10711-009-9425-7


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.


Log-canonical thresholdEnriques diagramNewton polygon

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  2. 2.Şcoala Normală SuperioarăBucharestRomania
  3. 3.Université d’AngersAngersFrance