On the uniqueness of (p, h)-gonal automorphisms of Riemann surfaces

摘要

Let X be a compact Riemann surface of genus g ≥ 2. A cyclic subgroup of prime order p of Aut(X) is called properly (p, h)-gonal if it has a fixed point and the quotient surface has genus h. We show that if p > 6h + 6, then a properly (p, h)-gonal subgroup of Aut(X) is unique. We also discuss some related results.