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arXiv · 2208.12013

Moishezon manifolds with no nef and big classes

Jia Jia·Sheng Meng
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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-isomorphic bimeromorphic map $f\colon X\dashrightarrow Y$ isomorphic in codimension $1$ to a compact K\"ahler 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., (2022): 1--11).

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Jia Jia, Sheng Meng. 2022-08-25. Moishezon manifolds with no nef and big classes. https://doi.org/10.1017/s0013091524000762

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