On the complement of nef divisors on projective manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908678052904960 |
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| author | Feklistov, S. |
| author_facet | Feklistov, S. |
| contents | Let $X'$ be a complex projective manifold, $\dim X'>1$, $Z$ a connected analytic subset of codimension one which is the support of a nef effective Cartier divisor $D$ on $X'$, $X:=X'\setminus Z$. Let $κ(D)$ be the Iitaka dimension of $D$. We prove that $X$ is not Hartogs if and only if $D$ is abundant and $κ(D)=1$. In particular, $X$ is not Hartogs if and only if $X$ is a proper fibration over an affine curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10730 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the complement of nef divisors on projective manifolds Feklistov, S. Algebraic Geometry Complex Variables [2010]Primary 32D20, 32L10, 32C35, 14C20, 14D06, Secondary 14J70, 32J15 Let $X'$ be a complex projective manifold, $\dim X'>1$, $Z$ a connected analytic subset of codimension one which is the support of a nef effective Cartier divisor $D$ on $X'$, $X:=X'\setminus Z$. Let $κ(D)$ be the Iitaka dimension of $D$. We prove that $X$ is not Hartogs if and only if $D$ is abundant and $κ(D)=1$. In particular, $X$ is not Hartogs if and only if $X$ is a proper fibration over an affine curve. |
| title | On the complement of nef divisors on projective manifolds |
| topic | Algebraic Geometry Complex Variables [2010]Primary 32D20, 32L10, 32C35, 14C20, 14D06, Secondary 14J70, 32J15 |
| url | https://arxiv.org/abs/2505.10730 |