Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

The classification of surfaces of general type with nonbirational bicanonical map


Author: Giuseppe Borrelli
Journal: J. Algebraic Geom. 16 (2007), 625-669
DOI: https://doi.org/10.1090/S1056-3911-07-00478-X
Published electronically: June 12, 2007
MathSciNet review: 2357686
Full-text PDF

Abstract | References | Additional Information

Abstract: We classify surfaces of general type whose bicanonical map factors through a rational map of degree 2 to a rational or ruled surface.

We prove that if such a surface has no pencil of genus 2 curves, then it is the smooth minimal model of a double plane branched along a reduced curve with certain singularities, a configuration already suggested by Du Val in the 1950s. This result allows us to complete the classification of surfaces of general type presenting the nonstandard case, with the possible exception of those with $ p_g=q\le 1$.


References [Enhancements On Off] (What's this?)


Additional Information

Giuseppe Borrelli
Affiliation: Departamento de Matematica, Universidade Federal de Pernambuco, Cidade Universitaria, 50740-540 Recife–PE, Brasil
Email: borrelli@dmat.ufpe.br

DOI: https://doi.org/10.1090/S1056-3911-07-00478-X
Received by editor(s): January 6, 2004
Received by editor(s) in revised form: February 16, 2007
Published electronically: June 12, 2007
Additional Notes: This work was partially supported by EU Research Training Network EAGER (HPRN-CT-2000-00099).
Dedicated: Dedicated to the memory of Professor Paolo Francia

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website