On the space of projective curves of maximal regularity

Kiryong Chung, Wanseok Lee, Euisung Park

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)505-518
Number of pages14
JournalManuscripta Mathematica
Volume151
Issue number3-4
DOIs
Publication statusPublished - 2016 Nov 1

Bibliographical note

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

Keywords

  • 51N35
  • Primary 14H45
  • Secondary 14D23

ASJC Scopus subject areas

  • General Mathematics

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