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On the set of divisors with zero geometric defect

  • Dinh Tuan Huynh and Duc-Viet Vu ORCID logo EMAIL logo
Published/Copyright: July 11, 2020

Abstract

Let f : 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 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.

Funding statement: Duc-Viet Vu is supported by a postdoctoral fellowship of the Alexander von Humboldt Foundation.

Acknowledgements

We would like to thank Tien-Cuong Dinh, Si Duc Quang and Song-Yan Xie for fruitful discussions. We also want to express our gratitude to the referee for comments which improved the presentation of the paper. Dinh Tuan Huynh is grateful to the Max Planck Institute for Mathematics in Bonn for its hospitality and financial support. He also wants to acknowledge the support from Hue University.

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Received: 2020-03-08
Revised: 2020-05-03
Published Online: 2020-07-11
Published in Print: 2021-02-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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