The curve $\tilde{\mathcal {C}}_4=(\lambda ^4, \lambda ^3 \mu , \lambda \mu ^3, \mu ^4) \subset \mathbb {P}^3_k$ , is not set-theoretic complete intersection of two quartic surfaces

A centrally symmetric plane curve has a point called it’s centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in $R^{3}$ . We investigate some of it’s properties, and begin the study of non-convex cases.

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