General elephants of three-fold divisorial contractions

Kawakita, Masayuki

doi:10.1090/S0894-0347-02-00416-2

General elephants of three-fold divisorial contractions
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by Masayuki Kawakita

J. Amer. Math. Soc. 16 (2003), 331-362

DOI: https://doi.org/10.1090/S0894-0347-02-00416-2

Published electronically: December 2, 2002

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Abstract:

We treat three-fold divisorial contractions whose exceptional divisors contract to Gorenstein points. We prove that a general element in the anti-canonical system around the exceptional divisor has at worst Du Val singularities. As application to classification, we describe divisorial contractions to compound $A_{n}$ points, and moreover, we deduce that any divisorial contraction to a compound $D_{n}$ or $E_{n}$ point has discrepancy $\le 4$.

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