## Abstract

Let Γ _{r} _{,} _{d} be the space of smooth rational curves of degree d in P^{r} of maximal regularity. Then the automorphism group Aut (P^{r}) = PGL (r+ 1) acts naturally on Γ _{r} _{,} _{d} and thus the quotient Γ _{r} _{,} _{d}/ PGL (r+ 1) classifies those rational curves up to projective motions. In this paper, we show that Γ _{r} _{,} _{d} is an irreducible variety of dimension 3 d+ r^{2}- r- 1. The main idea of the proof is to use the canonical form of rational curves of maximal regularity which is given by the (d- r+ 2) -secant line. Also, through the geometric invariant theory, we discuss how to give a scheme structure on the PGL (r+ 1) -orbits of rational curves.

Original language | English |
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Pages (from-to) | 505-518 |

Number of pages | 14 |

Journal | Manuscripta Mathematica |

Volume | 151 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2016 Nov 1 |

## Keywords

- 51N35
- Primary 14H45
- Secondary 14D23

## ASJC Scopus subject areas

- Mathematics(all)