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New canonical triple covers of surfaces

Author: Carlos Rito
Journal: Proc. Amer. Math. Soc. 143 (2015), 4647-4653
MSC (2010): Primary 14J29
Published electronically: March 31, 2015
MathSciNet review: 3391024
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Abstract: We construct a surface of general type with canonical map of degree $ 12$ which factors as a triple cover and a bidouble cover of $ \mathbb{P}^2$. We also show the existence of a smooth surface with $ q=0,$ $ \chi =13$ and $ K^2=9\chi $ such that its canonical map is either of degree $ 3$ onto a surface of general type or of degree $ 9$ onto a rational surface.

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Carlos Rito
Affiliation: Universidade de Trás-os-Montes e Alto Douro, UTAD, Quinta de Prados, 5000-801 Vila Real, Portugal,
Address at time of publication: Departamento de Matemática, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, Apartado 1013, 4169-007 Porto, Portugal,

Received by editor(s): November 4, 2013
Received by editor(s) in revised form: July 31, 2014
Published electronically: March 31, 2015
Additional Notes: The author wishes to thank Margarida Mendes Lopes, Sai-Kee Yeung, Gopal Prasad, Donald Cartwright, Tim Steger and especially Amir Dzambic and Rita Pardini for useful correspondence. The author is a member of the Center for Mathematics of the University of Porto. This research was partially supported by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT–Fundação para a Ciência e a Tecnologia under the projects PEst–C/MAT/UI0144/2013 and PTDC/MAT-GEO/0675/2012.
Communicated by: Lev Borisov
Article copyright: © Copyright 2015 American Mathematical Society

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