Automorphisms of $P_8$ Singularities and the Complex Crystallographic Groups

The paper completes the study of symmetries of parabolic function singularities with relation to complex crystallographic groups that was started by the first co-author and his collaborator. We classify smoothable automorphisms of $P_8$ singularities which split the kernel of the intersection form on the second homology. For such automorphisms, the monodromy groups acting on the duals to the eigenspaces with degenerate intersection form are then identified as some of complex affine reflection groups tabled by V. L. Popov.