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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Projective threefolds on which $\mathbf{SL}(2)$ acts with
2-dimensional general orbits


Author: T. Nakano
Journal: Trans. Amer. Math. Soc. 350 (1998), 2903-2924
MSC (1991): Primary 14L30; Secondary 14E30
MathSciNet review: 1451611
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Abstract: The birational geometry of projective threefolds on which $\mathbf{SL}(2)$ acts with 2-dimensional general orbits is studied from the viewpoint of the minimal model theory of projective threefolds. These threefolds are closely related to the minimal rational threefolds classified by Enriques, Fano and Umemura. The main results are (i) the $\mathbf{SL}(2)$-birational classification of such threefolds and (ii) the classification of relatively minimal models in the fixed point free cases.


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Additional Information

T. Nakano
Affiliation: Department of Mathematical Sciences, College of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Hiki-gun, Saitama-ken, 350-0394, Japan
Email: nakano@r.dendai.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02081-9
PII: S 0002-9947(98)02081-9
Keywords: $\mathbf{SL}(2)$-action, projective threefolds, minimal models
Received by editor(s): July 20, 1996
Article copyright: © Copyright 1998 American Mathematical Society