A Class of Pseudo-Real Riemann Surfaces with Diagonal Automorphism Group

• 作者: Eslam Badr
• 来源期刊: 代数集刊（英文版）
• 关键词: pseudo-real Riemann surface field of moduli field of definition plane curve automorphism group
• 年，卷（期）: 2020,（2）
• 页码范围: 247-262
• 页数: 16页
• 语种: 英文
• DOI: 10.1142/S1005386720000206

摘要

A Riemann surface S having field of moduli R,but not a field of definition,is called pseudo-real.This means that S has anticonformal automorphisms,but none of them is an involution.A Riemann surface is said to be plane if it can be described by a smooth plane model of some degree d ≥ 4 in P2C.We characterize pseudo-real-plane Riemann surfaces S,whose conformal automorphism group Aut+(S) is PGL3(C)-conjugate to a finite non-trivial group that leaves invariant infinitely many points of P2C.In particular,we show that such pseudo-real-plane Riemann surfaces exist only if Aut+(S) is cyclic of even order n dividing the degree d.Explicit families of pseudo-real-plane Riemann surfaces are given for any degree d =2pm with m ＞ 1 odd,p prime and n =d/p.