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2021 Examples of Surfaces with Canonical Map of Maximal Degree
Ching-Jui Lai, Sai-Kee Yeung
Taiwanese J. Math. Advance Publication 1-18 (2021). DOI: 10.11650/tjm/210105


It was shown by Beauville that if the canonical map $\varphi_{|K_M|}$ of a complex smooth projective surface $M$ is generically finite, then $\operatorname{deg}(\varphi_{|K_M|}) \leq 36$. The first example of a surface with canonical degree $36$ was found by the second author. In this article, we show that for any surface which is a degree four Galois étale cover of a fake projective plane $X$ with the largest possible automorphism group $\operatorname{Aut}(X) = C_7:C_3$ (the unique non-abelian group of order $21$), the base locus of the canonical map is finite, and we verify that $35$ of these surfaces have maximal canonical degree $36$. We also classify all smooth degree four Galois étale covers of fake projective planes, which give possible candidates for surfaces of canonical degree $36$. Finally, we also confirm in this paper the optimal upper bound of the canonical degree of smooth threefolds of general type with sufficiently large geometric genus, related to earlier work of Hacon and Cai.


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Ching-Jui Lai. Sai-Kee Yeung. "Examples of Surfaces with Canonical Map of Maximal Degree." Taiwanese J. Math. Advance Publication 1 - 18, 2021.


Published: 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.11650/tjm/210105

Primary: 14J25, 14J29

Rights: Copyright © 2021 The Mathematical Society of the Republic of China


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