Some examples of algebraic surfaces with canonical map of degree 20

Nguyen Bin

doi:10.5802/crmath.267

Algebraic geometry

Some examples of algebraic surfaces with canonical map of degree 20

Nguyen Bin ¹

¹ Mathematics Division, National Center for Theoretical Sciences, Taiwan

Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1145-1153.

Abstract

In this note, we construct two minimal surfaces of general type with geometric genus $p_{g} = 3$ , irregularity $q = 0$ , self-intersection of the canonical divisor $K^{2} = 20, 24$ such that their canonical map is of degree $20$ . In one of these surfaces, the canonical linear system has a non-trivial fixed part. These surfaces, to our knowledge, are the first examples of minimal surfaces of general type with canonical map of degree $20$ .

Received: 2021-01-04
Revised: 2021-05-05
Accepted: 2021-09-05
Published online: 2021-11-03

DOI: 10.5802/crmath.267

Classification: 14J29

Author's affiliations:

Nguyen Bin ¹

¹ Mathematics Division, National Center for Theoretical Sciences, Taiwan

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Nguyen Bin},
     title = {Some examples of algebraic surfaces with canonical map of degree~20},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1145--1153},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {9},
     year = {2021},
     doi = {10.5802/crmath.267},
     language = {en},
}

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Nguyen Bin. Some examples of algebraic surfaces with canonical map of degree 20. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1145-1153. doi : 10.5802/crmath.267. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.267/

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