Complements of branch curves of generic projections of complete intersection surfaces are CAT(0), while the universal families for E6, E7, and E8 singularities are not CAT(0).
Non-positively curved aspects of A rtin groups of finite type
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CAT(0) geometry of complex curve complements and families
Complements of branch curves of generic projections of complete intersection surfaces are CAT(0), while the universal families for E6, E7, and E8 singularities are not CAT(0).