Open Access
February, 2022 On the Syzygies of Ample Line Bundles on Fake Projective Planes
Sui-Chung Ng, Sai-Kee Yeung
Author Affiliations +
Taiwanese J. Math. 26(1): 49-67 (February, 2022). DOI: 10.11650/tjm/210901


Our goal is to study the syzygies of the projective embeddings defined by the ample line bundles on a fake projective plane $S$. The syzygies are studied in terms of the property $N_p$. For various kinds of ample line bundles, we give explicit lower bounds for their powers above which the property $N_p$ is satisfied.

Funding Statement

The first author was partially supported by National Natural Science Foundation of China (Grant No. 11501205) and Science and Technology Commission of Shanghai Municipality (Grant No. 13dz2260400). The second author was partially supported by grants from the National Science Foundation, USA.


It is a pleasure for the authors to thank Donald Cartwright for providing computer data files for the proof of Theorem 4.2 which leads to Theorem 1.5 and thank Lawrence Ein and Jun-Muk Hwang for fruitful discussions and providing very useful references. They would also like to thank the anonymous referees for carefully reading the paper and giving helpful suggestions.


Download Citation

Sui-Chung Ng. Sai-Kee Yeung. "On the Syzygies of Ample Line Bundles on Fake Projective Planes." Taiwanese J. Math. 26 (1) 49 - 67, February, 2022.


Received: 25 December 2020; Revised: 27 August 2021; Accepted: 5 September 2021; Published: February, 2022
First available in Project Euclid: 14 September 2021

MathSciNet: MR4367786
zbMATH: 1487.13033
Digital Object Identifier: 10.11650/tjm/210901

Primary: 13D02 , 14C20 , 14J29

Keywords: fake projective planes , pluricanonical mappings , Syzygies

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

Vol.26 • No. 1 • February, 2022
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