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April 2023 Singularity of normal complex analytic surfaces admitting non-isomorphic finite surjective endomorphisms
Noboru Nakayama
Author Affiliations +
Osaka J. Math. 60(2): 403-489 (April 2023).

Abstract

For a non-isomorphic finite endomorphism of a germ of a complex analytic normal surface at a point, the pair of the surface and a completely invariant reduced divisor is shown to be log-canonical. It is also shown in many situations that the endomorphism or its square lifts to an endomorphism of another surface by an essential blowing up.

Acknowledgments

The author is grateful to Professor Charles Favre for sending a preprint version of [6] with communication by e-mail. The author thanks Professors Yoshio Fujimoto and De-Qi Zhang for the discussion on this subject in seminars at Research Institute for Mathematical Sciences, Kyoto University. The author is grateful to the referee for comments and suggestions. The author is partially supported by Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.

Citation

Download Citation

Noboru Nakayama. "Singularity of normal complex analytic surfaces admitting non-isomorphic finite surjective endomorphisms." Osaka J. Math. 60 (2) 403 - 489, April 2023.

Information

Received: 15 April 2021; Revised: 12 January 2022; Published: April 2023
First available in Project Euclid: 3 April 2023

MathSciNet: MR4572548
zbMATH: 1517.32099

Subjects:
Primary: 32S25
Secondary: 32H50

Rights: Copyright © 2023 Osaka University and Osaka Metropolitan University, Departments of Mathematics

Vol.60 • No. 2 • April 2023
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