Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Surfaces with canonical map of maximum degree


Author: Carlos Rito
Journal: J. Algebraic Geom.
DOI: https://doi.org/10.1090/jag/761
Published electronically: September 13, 2021
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Abstract: We use the Borisov-Keum equations of a fake projective plane and the Borisov-Yeung equations of the Cartwright-Steger surface to show the existence of a regular surface with canonical map of degree 36 and of an irregular surface with canonical map of degree 27. As a by-product, we get equations (over a finite field) for the $\mathbb {Z}/3$-invariant fibres of the Albanese fibration of the Cartwright-Steger surface and show that they are smooth.


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Carlos Rito
Affiliation: Universidade de Trás-os-Montes e Alto Douro, UTAD, Quinta de Prados, 5000-801 Vila Real, Portugal; and Departamento de Matemática, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
MR Author ID: 744585
Email: crito@utad.pt; and crito@fc.up.pt

Received by editor(s): September 24, 2019
Received by editor(s) in revised form: December 19, 2019
Published electronically: September 13, 2021
Additional Notes: This research was supported by FCT (Portugal) under the project PTDC/MAT-GEO/2823/2014, the fellowship SFRH/BPD/111131/2015 and by CMUP (UIDB/00144/2020), which is funded by FCT with national (MCTES) and European structural funds through the programs FEDER, under the partnership agreement PT2020.
Article copyright: © Copyright 2021 University Press, Inc.