A note on polarized varieties with high nef value
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Zhining Liu
Abstract
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.
Acknowledgements
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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Articles in the same Issue
- Frontmatter
- Duality related with key varieties of ℚ-Fano threefolds constructed from projective bundles
- Continuous CM-regularity and generic vanishing
- Quotient spaces of K3 surfaces by non-symplectic involutions fixing a curve of genus 8 or more
- A note on polarized varieties with high nef value
- Anisotropic area-preserving nonlocal flow for closed convex plane curves
- New sextics of genus 6 and 10 attaining the Serre bound
- The balanced superelliptic mapping class groups are generated by three elements
- Bach flow of simply connected nilmanifolds
Articles in the same Issue
- Frontmatter
- Duality related with key varieties of ℚ-Fano threefolds constructed from projective bundles
- Continuous CM-regularity and generic vanishing
- Quotient spaces of K3 surfaces by non-symplectic involutions fixing a curve of genus 8 or more
- A note on polarized varieties with high nef value
- Anisotropic area-preserving nonlocal flow for closed convex plane curves
- New sextics of genus 6 and 10 attaining the Serre bound
- The balanced superelliptic mapping class groups are generated by three elements
- Bach flow of simply connected nilmanifolds
