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 | References | Similar Articles | Additional Information

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 points, and moreover, we deduce that any divisorial contraction to a compound or point has discrepancy .

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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