Abstract
We derive asymptotically proper sufficient conditions for the existence of hypersurfaces W ⊂ ℙ n with prescribed simple singularities. By first constructing hypersurfaces with one simple singularity of type S corresponding to a T-smooth germ of V d (S), d = deg(W), and then applying a version of Viro's method we show how to construct hypersurfaces of degree d with simple singularities of types S 1,…, S r whenever
Acknowledgments
I would like to thank Prof. E. Shustin (Tel Aviv University), Prof. G.-M. Greuel, and Dr. C. Lossen (University of Kaiserslautern) for many fruitful discussions and suggestions.
The methods used in this paper are based to some extent on a preprint of Prof. E. Shustin, now published in Shustin (Citation2000), and I am very grateful to him for providing his material before publication. The author is supported by grant GR-640/9-1 DFG-Schwerpunkt, “Globale Methoden in der komplexen Geometrie.”