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

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

2001-10-04

arxiv.org/abs/math/0110050v1

Mathematics

Algebraic Geometry

41 pages

Scientific paper

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 A_n points, and moreover we conclude that discrepancies of divisorial contractions to compound D_n or E_n points are at most four.

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