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

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

2005-05-11

arxiv.org/abs/math/0505231v2

Mathematics

Algebraic Geometry

Final version to appear in Proceedings of the AMS

Scientific paper

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 is a morphism, then the degree of the bicanonical map of S is not equal to 3. This completes our earlier results, showing that if X is a minimal surface of general type with p_g=0, K^2>=3 such that |2K_X| is free, then the bicanonical map of X can have degree 1, 2 or 4.

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