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  On the set of divisors with zero geometric defect

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0007-ABF5-4 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-0781-8
Genre: Journal Article

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arXiv:1907.08740.pdf (Preprint), 247KB
 
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 Creators:
Huynh, Dinh Tuan1, Author           
Vu, Duc-Viet, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Complex Variables, Algebraic Geometry, Dynamical Systems
 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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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 1907.08740
DOI: 10.1515/crelle-2020-0017
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Title: Journal für die reine und angewandte Mathematik
  Abbreviation : J. reine angew. Math.
Source Genre: Journal
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Publ. Info: De Gruyter
Pages: - Volume / Issue: 771 Sequence Number: - Start / End Page: 193 - 213 Identifier: -