Orders of automorphisms of smooth plane curves for the automorphism groups to be cyclic

Abstract For a fixed integer $$d\ge 4$$ d ≥ 4 , the list of groups that appear as automorphism smooth plane curves whose degree is d unknown, except for $$d=4$$ = or 5. Harui showed certain characteristic about structures curves. Badr and Bars began to study orders automorphisms try obtain exact In this paper, based on result T. Harui, we extend Badr–Bars different new cases, mainly cases cyclic groups.