A Riemann surface S having field of moduli M,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 plan...A Riemann surface S having field of moduli M,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 P^2/C.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 P^2/C.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-reai-plane Riemann surfaces are given for any degree d=2pm with m>1 odd,p prime and n=d/p.展开更多
文摘A Riemann surface S having field of moduli M,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 P^2/C.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 P^2/C.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-reai-plane Riemann surfaces are given for any degree d=2pm with m>1 odd,p prime and n=d/p.
