On isolated log canonical singularities with index one

Abstract

We give a method to investigate isolated log canonical singularities with index one which are not log terminal. Our method depends on the minimal model program. One of the main purposes is to prove that our invariant coincides with Ishii's Hodge theoretic invariant.

22 pages, v2: revision following referee's comments, v3: very minor revision, v4: very minor revision, v5: final version, to appear in J. Math. Sci. Univ. Tokyo, v5: typos in Remark 5.3 were corrected