Automorphism Groups of Symmetric and Pseudo-real Riemann Surfaces

Abstract The category of smooth, irreducible, projective, complex algebraic curves is equivalent to the compact Riemann surfaces. We study automorphism groups surfaces which are with real moduli. A curve C has moduli when corresponding surface $$X_C$$ X C admits an anti-conformal automorphism. If no such involution (symmetry), then called pseudo-real and isomorphic its conjugate, but not definable over reals. Otherwise, symmetric real.