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In this paper we study ideals of points lying on rational normal curvesdefined in projective plane and projective $ 3 $-space. We give an explicitformula for the value of Castelnuovo-Mumford regularity for their ordinarypowers. Moreover, we compare the $ m $-th symbolic and ordinary powers for suchideals in order to show whenever the $ m $-th symbolic defect is non-zero.

Regularity and symbolic defect of points on rational normal curves