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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The degree of the bicanonical map of a surface with $ p_g=0$


Authors: Margarida Mendes Lopes and Rita Pardini
Journal: Proc. Amer. Math. Soc. 135 (2007), 1279-1282
MSC (2000): Primary 14J29
Published electronically: November 13, 2006
MathSciNet review: 2276635
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Abstract: In this note it is shown that, given a smooth minimal complex surface of general type $ S$ with $ p_g(S)=0$, $ K^2_S=3$, for which the bicanonical map $ \varphi _{2K}$ is a morphism, the degree of $ \varphi _{2K}$ is not 3. This completes our earlier results, showing that if $ S$ is a minimal surface of general type with $ p_g=0$, $ K^2\ge 3$ such that $ \vert 2K_S\vert$ is free, then the bicanonical map of $ S$ can have degree 1, 2 or 4.


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Margarida Mendes Lopes
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Email: mmlopes@math.ist.utl.pt

Rita Pardini
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, 56127 Pisa, Italy
Email: pardini@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08633-3
PII: S 0002-9939(06)08633-3
Received by editor(s): May 11, 2005
Received by editor(s) in revised form: December 16, 2005
Published electronically: November 13, 2006
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.