Periodic surface automorphisms and algebraic independence of Morita–Mumford classes

We prove a vanishing theorem for the Morita–Mumford classes on periodic surface automorphisms, and construct enough periodic automorphisms to give an alternative and elementary proof of the stable rational algebraic independence of the Morita–Mumford classes, originally shown by Miller (J. Differential Geom. 24 (1986) 1–14) and Morita (Invent. Math. 90 (1987) 551–557).