On the space of projective curves of maximal regularity

Abstract

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