On the set of divisors with zero geometric defect

Dinh Tuan Huynh; Duc-Viet Vu

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arXiv · 1907.08740

On the set of divisors with zero geometric defect

Dinh Tuan Huynh·Duc-Viet Vu

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Abstract

Let $f: \mathbb{C} \to X$ be a transcendental holomorphic curve into a complex projective manifold $X$. Let $L$ be a very ample line bundle on $X$. Let $s$ be a very generic holomorphic section of $L$ and $D$ the zero divisor given by $s$. We prove that the \emph{geometric} defect of $D$ (defect of truncation $1$) with respect to $f$ is zero. We also prove that $f$ almost misses general enough analytic subsets on $X$ of codimension $2$.

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Dinh Tuan Huynh, Duc-Viet Vu. 2019-07-20. On the set of divisors with zero geometric defect. https://arxiv.org/abs/1907.08740

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