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January 2022 Some remarks on finiteness of extremal rays of divisorial type
Yoshio Fujimoto
Proc. Japan Acad. Ser. A Math. Sci. 98(1): 7-12 (January 2022). DOI: 10.3792/pjaa.98.002

Abstract

Let $X$ be a normal $\mathbf{Q}$-factorial projective variety with at most log canonical singularities. We shall give a sufficient condition for the existence of at most finitely many $K_{X}$-negative extremal rays $R(\subset \overline{\mathrm{NE}}(X))$ of divisorial type. As an application, we show that for a nonisomorphic surjective endomorphism $f\colon X\to X$ of a normal projective $\mathbf{Q}$-factorial terminal 3-fold $X$ with $\kappa(X) > 0$, a suitable power $f^{k}\ (k > 0)$ of $f$ descends to a nonisomorphic surjective endomorphism $g\colon X_{\textit{min}}\to X_{\textit{min}}$ of a minimal model $X_{\textit{min}}$ of $X$.

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Yoshio Fujimoto. "Some remarks on finiteness of extremal rays of divisorial type." Proc. Japan Acad. Ser. A Math. Sci. 98 (1) 7 - 12, January 2022. https://doi.org/10.3792/pjaa.98.002

Information

Published: January 2022
First available in Project Euclid: 4 March 2022

Digital Object Identifier: 10.3792/pjaa.98.002

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

Keywords: divisorial contraction , endomorphism , extremal ray , flip , termination

Rights: Copyright © 2022 The Japan Academy

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Vol.98 • No. 1 • January 2022
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