Regularity and symbolic defect of points on rational normal curves

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

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