Simple singularity of type E7 and the complex reflection group ST34
Abstract
This paper studies a family of surfaces of C3 which is a deformation of a simple singularity of type E7. This family has six parameters which are regarded as basic invariants of the complex reflection group No.34 in the list of the paper of Shephard and Todd ST. We compute 1-parameter subfamilies of the family in question corresponding to corank one reflection subgroups of No.34 group. In particular, we determine the types of simple singularities on the surfaces appeared in this manner.
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