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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. 31 (2022), 127-135
Published electronically: September 13, 2021
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Abstract | References | Additional Information

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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Additional Information

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:; and

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.
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