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Moishezon manifolds with no nef and big classes

Part of: Automorphic functions Complex spaces with a group of automorphisms Compact analytic spaces

Published online by Cambridge University Press:  26 November 2024

Jia Jia Open the ORCID record for Jia Jia [Opens in a new window]  and
Sheng Meng
Jia Jia*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore Yau Mathematical Sciences Center, Jingzhai, Tsinghua University, Beijing, China
Sheng Meng
Affiliation:
School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, People’s Republic of China Korea Institute For Advanced Study, Seoul, Republic of Korea
*
Corresponding author: Jia Jia, email: jia_jia@u.nus.edu; mathjiajia@tsinghua.edu.cn
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Abstract

We show that a compact complex manifold X has no non-trivial nef $(1,1)$-classes if there is a non-biholomorphic bimeromorphic map $f\colon X\dashrightarrow Y$, which is an isomorphism in codimension 1 to a compact Kähler manifold Y with $h^{1,1}=1$. In particular, there exist infinitely many isomorphic classes of smooth compact Moishezon threefolds with no nef and big $(1,1)$-classes. This contradicts a recent paper (Strongly Jordan property and free actions of non-abelian free groups, Proc. Edinb. Math. Soc., 65(3) (2022), 736–746).

Keywords

Moishezon spaceFujiki’s class 𝒞nef and big

MSC classification

Primary: 32J27: Compact Kähler manifolds
Secondary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 68 , Issue 1 , February 2025 , pp. 198 - 204
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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