On the set of divisors with zero geometric defect

Huynh, Dinh Tuan; Vu, Duc-Viet

doi:10.1515/crelle-2020-0017

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On the set of divisors with zero geometric defect

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Huynh, Dinh Tuan
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1515/crelle-2020-0017
(Publisher version)

https://doi.org/10.48550/arXiv.1907.08740
(Preprint)

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Citation

Huynh, D. T., & Vu, D.-V. (2021). On the set of divisors with zero geometric defect. Journal für die reine und angewandte Mathematik, 771, 193-213. doi:10.1515/crelle-2020-0017.

Cite as: https://hdl.handle.net/21.11116/0000-0007-ABF5-4

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 $2$.