Involutions on surfaces with \(p_g = q = 1\) (Q847031)

The paper deals with the classification of complex surfaces of general type with \(p_g=q=1\) having an involution \(i\). The further assumption that the bicanonical map is not composed with \(i\) is done. Under such hypotheses the author lists all the possible quotient surfaces \(S/i\) and branch curves. He also constructs some of the examples using bidouble covers of ruled surfaces. The existence of the branch curves with the right multiplicities is verified using \texttt{MAGMA}.