Extremal disks and extremal surfaces of genus three

Kodai Mathematical Journal

Gou Nakamura¹ 

[1] SCIENCE DIVISION CENTER FOR GENERAL EDUCATION AICHI INSTITUTE OF TECHNOLOGY

关键词: extremal disk;    extremal surface;    the group of automorphisms;    hyperelliptic surface;    Weierstrass point;   

DOI  :  10.2996/kmj/1111588041

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(9)A compact Riemann surface of genus g≥2 is said to be extremal if it admits an extremal disk, a disk of the maximal radius determined by g. If g=2 or g≥4, it is known that how many extremal disks an extremal surface of genus g can admit. In the present paper we deal with the case of g=3. Considering the side-pairing patterns of the fundamental polygons, we show that extremal surfaces of genus 3 admit at most two extremal disks and that 16 surfaces admit exactly two. Also we describe the group of automorphisms and hyperelliptic surfaces.

【 授权许可】

Unknown