Moishezon manifolds with no nef and big classes
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913706069196800 |
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| author | Jia, Jia Meng, Sheng |
| author_facet | Jia, Jia Meng, Sheng |
| contents | 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 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., (2022): 1--11). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_12013 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Moishezon manifolds with no nef and big classes Jia, Jia Meng, Sheng Algebraic Geometry Complex Variables 32J27, 32M05 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 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., (2022): 1--11). |
| title | Moishezon manifolds with no nef and big classes |
| topic | Algebraic Geometry Complex Variables 32J27, 32M05 |
| url | https://arxiv.org/abs/2208.12013 |