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arXiv · 2505.10730

On the complement of nef divisors on projective manifolds

S. Feklistov
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Abstract

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 $\kappa(D)$ be the Iitaka dimension of $D$. We prove that $X$ is not Hartogs if and only if $D$ is abundant and $\kappa(D)=1$. In particular, $X$ is not Hartogs if and only if $X$ is a proper fibration over an affine curve.

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S. Feklistov. 2025-05-15. On the complement of nef divisors on projective manifolds. https://arxiv.org/abs/2505.10730

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