Abstract
We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups. As a result, we improve some lower bounds on the number of singularities of a given type that a plane curve or a surface in of a given degree might have.
Acknowledgments
I wish to thank warmly Alessandra Sarti, Oliver Labs and Duco van Straten for useful comments and references and Gunter Malle for a careful reading of a first version of this paper. Figures were realized using the software SURFER [Citationimaginary].
Notes
1 There is an important exception to this remark: all the singular points of the surface of degree 8 with 48 singularities of type D4 constructed in Example 5.3 have rational coordinates.
2 Some Milnor and Tjurina numbers were computed with SINGULAR [CitationDecker et al. 18].