RATIONALITY OF THE OFFSETS TO ALGEBRAIC CURVES AND SURFACES

simple method is developed to identify the rationality of offsets to algebraic curves and surfaces which are gived either implicitly or parametrically and to parametrize the offsets if they are rational. In particular,we show that offsets to ellipses and hyperbolas are of nonzero genus except for the circles,and somewhat surprisingly,that offsets to paraboloids and hyperboloids with one sheet can all be rationally parametrized.