Abstract
Let Γ r , d be the space of smooth rational curves of degree d in Pr of maximal regularity. Then the automorphism group Aut (Pr) = 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+ r2- 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 |
---|---|
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)