General elements in anticanonical systems of threefolds with divisorial contractions and applications to classification
Masayuki Kawakita
Abstract
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.
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