The degree of the bicanonical map of a surface with $p_g=0$
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- by Margarida Mendes Lopes and Rita Pardini PDF
- Proc. Amer. Math. Soc. 135 (2007), 1279-1282 Request permission
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 $|2K_S|$ is free, then the bicanonical map of $S$ can have degree 1, 2 or 4.References
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Additional Information
- 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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1279-1282
- MSC (2000): Primary 14J29
- DOI: https://doi.org/10.1090/S0002-9939-06-08633-3
- MathSciNet review: 2276635