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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Classification of extremal contractions
from smooth fourfolds of $(3,1)$-type


Author: Hiromichi Takagi
Journal: Proc. Amer. Math. Soc. 127 (1999), 315-321
MSC (1991): Primary 14E30; Secondary 14J35
MathSciNet review: 1637436
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Abstract: We investigate divisorial contractions of extremal rays from
smooth fourfolds. When the exceptional divisor is contracted to a curve, we prove that the divisor is a $\mathbb{P}^{2}$-bundle or quadric bundle over a smooth curve and the contraction is the blowing up along the curve. Furthermore we determine the local analytic structure of the contraction.


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Additional Information

Hiromichi Takagi
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-0041, Japan
Email: htakagi@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05114-X
PII: S 0002-9939(99)05114-X
Keywords: Extremal ray, contraction morphism
Received by editor(s): February 12, 1997
Received by editor(s) in revised form: April 24, 1997
Additional Notes: The author is a Research Fellow of the Japan Society for the Promotion of Science
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society