Matrix Classes Realized by Automorphisms of Compact Riemann Surfaces of Genus Two

Abstract

A complete list of realizable conjugacy classes of torsion in the 4 × 4 integral symplectic group by analytic automorphisms of compact connected Riemann surfaces of genus two is given.

Key Words:

• Automorphism
• Fuchsian group
• Fundamental domain
• Integral symplectic matrix
• Riemann surface

2000 Mathematics Subject Classification:

• 20H25
• 57M60

ACKNOWLEDGMENT

We would like to thank the referee for his help on the article.

The project sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

Notes

Communicated by J. Zhang.