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Revista Matemática Complutense, 2005 This paper extends the results of \textit{E. Shustin} and \textit{E. Westenberger} [J. Lond. Math. Soc., II. Ser. 70, No. 3, 609--624 (2004; Zbl 1075.14034)] on the existence of algebraic hypersurfaces with prescribed simple singularities to the real case.
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