The log-canonical threshold of a plane curve

Abstract

We give an explicit formula for the log-canonical threshold of a reduced germ of plane curve. The formula depends only on the first two maximal contact values of the branches and their intersection multiplicities. We also improve the two branches formula given in a paper by Kuwata in Amer. J. Math. 121.

Changed Remark 6. Added two references. Minor changes in the introduction

Cited by in corpus (5)

• Shokurov's conjecture on conic bundles with canonical singularities
• Multiplicities of Jumping Numbers
• Enumerating odd-degree hyperelliptic curves and abelian surfaces over ${\mathbb{P}}^1$
• Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron
• The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces