Abstract
This article treats smooth weak Fano threefolds V having an extremal ray of type D. We further assume that the pluri-anti-canonical morphism of V contracts only a finite number of curves, i.e., the anti-canonical model of V is terminal. The contraction morphism corresponding to the extremal ray of type D is a del Pezzo fibration of degree d for \(1\leqslant d\leqslant 6\) or \(d=8,9\). Smooth weak Fano threefolds with an extremal ray of type D of degree \(\ne 6\) are classified into 47 deformation types.
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Acknowledgements
The author is grateful to Prof. Shigeru Mukai for pointing out various mistakes, to Prof. Shigefumi Mori for suggesting some ideas and correcting several missing terminology, and to Prof. Takashi Maeda and Prof. Hiromichi Takagi for valuable conversation.
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This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C)(2), 12640048, 2000-2001.
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Takeuchi, K. Weak Fano threefolds with del Pezzo fibration. European Journal of Mathematics 8, 1225–1290 (2022). https://doi.org/10.1007/s40879-022-00571-3
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DOI: https://doi.org/10.1007/s40879-022-00571-3