Automorphisms of $P_8$ singularities and the complex crystallographic groups

Details Automorphisms of $P_8$ singularities and the complex crystallographic groups Automorphisms of $P_8$ singularities and the complex crystallographic groups

2008-06-10

arxiv.org/abs/0806.1720v1

Proceedings of the Steklov Institute of Math, 2009 Vol.267 pp.91-103

Mathematics

Algebraic Geometry

Scientific paper

The paper completes the study of symmetries of parabolic function singularities with relation to complex crystallographic groups that was started in \cite{GM,X9}. 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 in \cite{P}.

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