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General elephants of three-fold divisorial contractions


Author: Masayuki Kawakita
Journal: J. Amer. Math. Soc. 16 (2003), 331-362
MSC (2000): Primary 14E05, 14E30
DOI: https://doi.org/10.1090/S0894-0347-02-00416-2
Published electronically: December 2, 2002
MathSciNet review: 1949163
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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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Additional Information

Masayuki Kawakita
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
Email: kawakita@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0894-0347-02-00416-2
Keywords: General elephant, divisorial contraction
Received by editor(s): October 22, 2001
Received by editor(s) in revised form: September 4, 2002
Published electronically: December 2, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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