Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients
-
Sai-Kee Yeung
Abstract
The purpose of this note is to show that
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1501282
Funding statement: The author was partially supported by a grant from the National Science Foundation (grant no. DMS-1501282).
A Appendix
Here we list the fake projective planes according to types discussed in the proof of Theorem 5.1.
The naming of the fake projective planes is given according to the naming of Cartwright and Steger in [6].
There are altogether 50 lattices of
List of cases of fake projective planes.
| M | cases |
| (b) | |
| (b) | |
| (c) | |
| (b) | |
| (b) | |
| (c) | |
| (b) | |
| (d) | |
| (b) | |
| (b) | |
| (b) | |
| (b) | |
| (c) | |
| (b) | |
| (c) | |
| (b) | |
| (c) | |
| min type | |
| min type | |
| (b) | |
| (c) | |
| (b) | |
| (b) | |
| (b) | |
| (b) |
| M | cases |
| (c) | |
| (b) | |
| (b) | |
| (b) | |
| min type | |
| min type | |
| (b) | |
| (b) | |
| (b) | |
| (b) | |
| (c) | |
| (c) | |
| (b) | |
| (b) | |
| (b) | |
| (b) | |
| (b) | |
| (b) | |
| (b) | |
| (c) | |
| (b) | |
| (b) | |
| (c) | |
| (b) | |
| (c) |
Acknowledgements
The author is grateful to Lawrence Ein for raising the question about the Cartwright–Steger surfaces and for explaining the argument of Reider to the author, to Rong Du and Ching-Jui Lai for helpful discussions, to Fabrizio Catanese, and a referee for pointing out a gap in an earlier draft of this paper. It is a pleasure for the author to express his gratitude to the referees for very helpful comments and suggestions on the article.
References
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Articles in the same Issue
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- Towards a Goldberg–Shahidi pairing for classical groups
- On the non-existence of cyclic splitting fields for division algebras
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- Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients
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- A non-homogeneous local Tb theorem for Littlewood–Paley g*λ-function with Lp-testing condition
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- On symplectic semifield spreads of PG(5,q2), q odd
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Articles in the same Issue
- Frontmatter
- The variance of divisor sums in arithmetic progressions
- Characterizing Lie groups by controlling their zero-dimensional subgroups
- CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups
- Towards a Goldberg–Shahidi pairing for classical groups
- On the non-existence of cyclic splitting fields for division algebras
- Sequential motion planning algorithms in real projective spaces: An approach to their immersion dimension
- Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients
- Anharmonic solutions to the Riccati equation and elliptic modular functions
- A non-homogeneous local Tb theorem for Littlewood–Paley g*λ-function with Lp-testing condition
- Saturation rank for finite group schemes: Finite groups and infinitesimal group schemes
- On symplectic semifield spreads of PG(5,q2), q odd
- From Freudenthal’s spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra
- Golodness and polyhedral products for two-dimensional simplicial complexes
