Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2009; 46(5): 917-930

Printed September 1, 2009

https://doi.org/10.4134/BKMS.2009.46.5.917

Copyright © The Korean Mathematical Society.

Isomorphism classes of genus-3 pointed trigonal curves over finite fields of characteristic $2$

Pyung-Lyun Kang and Sunmi Sun

Chungnam National University and Daejeon Gwanjeo High School

Abstract

We find all distinct representatives of isomorphism classes of genus-3 pointed trigonal curves and compute the number of isomorphism classes of a special class of genus-3 pointed trigonal curves including that of Picard curves over a finite field $F$ of characteristic $2$.

Keywords: isomorphism classes, genus-$3$ trigonal curves, Picard curve, finite fields of characteristic $2$

MSC numbers: 11G20

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