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January 2022 Étale endomorphisms of 3-folds. II
Yoshio Fujimoto
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Osaka J. Math. 59(1): 1-14 (January 2022).

Abstract

Up to a finite étale covering, we classify smooth projective $3$-folds $X$ with $\kappa(X) = -\infty$ admitting a nonisomorphic étale endomorphism in the case where there exists an FESP $Y_{\bullet}$ constructed from $X$ by a sequence of blowing-downs of an ESP and an extremal ray $R_{\bullet}$ of fiber type on $\operatorname{\overline{NE}}(Y_{\bullet})$ such that the pair $(Y_{\bullet}, R_{\bullet})$ is of type $(\text{C}_1)$ or $(\text{C}_0)$.

Acknowledgments

The author wishes to express sincire thanks to Professor Noboru Nakayama for many useful discussions and advices and to the referee for the careful reading of the manuscript. The author is supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.

Citation

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Yoshio Fujimoto. "Étale endomorphisms of 3-folds. II." Osaka J. Math. 59 (1) 1 - 14, January 2022.

Information

Received: 8 November 2017; Revised: 22 May 2019; Published: January 2022
First available in Project Euclid: 31 January 2022

Subjects:
Primary: 14E05 , 14E30 , 14J15 , 14J25 , 14J30 , 14J60
Secondary: 32J17

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

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Vol.59 • No. 1 • January 2022
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