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Moishezon manifolds with no nef and big classes
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 68 / Issue 1 / February 2025
- Published online by Cambridge University Press:
- 26 November 2024, pp. 198-204
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- Article
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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).
