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

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 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.

Final version to appear in Proceedings of the AMS