## 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 $\le 4$.## References

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## Bibliographic Information

**Masayuki Kawakita**- Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
- MR Author ID: 680001
- Email: kawakita@ms.u-tokyo.ac.jp
- Received by editor(s): October 22, 2001
- Received by editor(s) in revised form: September 4, 2002
- Published electronically: December 2, 2002
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1949163