General elements in anticanonical systems of threefolds with divisorial contractions and applications to classification

الأصل · EN

We treat threefolds with divisorial contractions whose exceptional divisors contract to compound Du Val points. We prove that general elements in their anticanonical systems around the exceptional divisors have at worst Du Val singularities. As applications to classification, we describe divisorial contractions to compound Aₙ points, and moreover we conclude that discrepancies of divisorial contractions to compound Dₙ or Eₙ points are at most four.