On the space of projective curves of maximal regularity

Let (Formula presented.) be the space of smooth rational curves of degree d in (Formula presented.) of maximal regularity. Then the automorphism group (Formula presented.) acts naturally on (Formula presented.) and thus the quotient (Formula presented.) classifies those rational curves up to projective motions. In this paper, we show that (Formula presented.) is an irreducible variety of dimension (Formula presented.). The main idea of the proof is to use the canonical form of rational curves of maximal regularity which is given by the (Formula presented.)-secant line. Also, through the geometric invariant theory, we discuss how to give a scheme structure on the (Formula presented.)-orbits of rational curves.