The classification of surfaces of general type with nonbirational bicanonical map

Borrelli, Giuseppe

doi:10.1090/S1056-3911-07-00478-X

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
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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 $p_g=q\le 1$.

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Additional Information

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

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