| Home  | About ScienceAsia  | Publication charge  | Advertise with us  | Subscription for printed version  | Contact us  
Editorial Board
Journal Policy
Instructions for Authors
Online submission
Author Login
Reviewer Login
Volume 43 Number 4
Volume 43 Number 3
Volume 43 Number 2
Volume 43 Number 1
Volume 43S Number 1
Volume 42 Number 6
Earlier issues
Volume 42 Number 5 Volume 42S Number 1

previous article next article 1

Research articles

ScienceAsia 42S(2016): 26-33 |doi: 10.2306/scienceasia1513-1874.2016.42S.026


Normal forms of smooth plane quartics and their restrictions


Takahashi˙Tadashi

 
ABSTRACT:     It is well known that smooth plane quartic curves in a two-dimensional complex projective space are curves of genus three and that the dimension of the parameters of the defining equation is less than seven. We show a process for obtaining the normal forms and their restrictions. For a homogeneous 4th-degree polynomial over the complex numbers, the vanishing set ℂ of the homogeneous polynomial in the complex projective plane ℙ2 is a curve of genus three, and such curves depend on six-dimensional parameters. By using the Gröbner basis of the elimination ideal, we show the restrictions on smooth plane quartics.

Download PDF

3 Download 73 View


Department˙of˙Intelligence˙and˙Informatics, Konan˙University, 8-9-1˙Okamoto, Higashinada, Kobe, Japan

* Corresponding author, E-mail: takahasi@konan-u.ac.jp

Received 31 Aug 2014, Accepted 20 Jul 2016