Recently, the classical Veronese surface reemerged in the context of the application oriented field of Computer Aided Geometric Design due to its interesting relation to rational triangular Bézier surfaces. This motivated the investigation of Veronese varieties presented in this paper. It is shown that the general degree \( n \) Veronese surface forms a singular subvariety of certain algebraic varieties. This general result is then further examined and extended in the low-degree cases \( n=2,3,4 \).
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