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A note on polarized varieties with high nef value

  • Zhining Liu EMAIL logo
From the journal Advances in Geometry


We study the classification problem for polarized varieties with high nef value. We give a complete list of isomorphism classes for normal polarized varieties with high nef value. This generalizes classical work on the smooth case by Fujita, Beltrametti and Sommese. As a consequence we obtain that polarized varieties with slc singularities and high nef value are birationally equivalent to projective bundles over nodal curves.

MSC 2010: 14C20


The article is part of my PhD thesis. I would like to express my sincere gratitude to my advisor Andreas Höring for his support and guidance, and for proposing this project to me. I also thank Enrica Floris for reading my rather awkward draft and making many suggestions to make the article more readable. I thank Stephan Druel for his comments. The results quoted in Remark 1.8 are told to me by S. Druel. I also thank my co-advisor Benoît Claudon for pointing out some errors and typos. I thank the referee for careful reading and valuable remarks and for having pointed out a mistake in Lemma 3.4 in the original manuscript. The essential part of this article was written when I was in Laboratoire J. A. Dieudonné. I thank the LJAD for its accommodation and its nice research environment.


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Received: 2023-05-08
Revised: 2023-08-26
Published Online: 2024-01-24
Published in Print: 2024-01-29

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