The codegree Turán density of 3-uniform tight cycles

Given any ε > 0 we prove that every sufficiently large n -vertex 3-graph H where every pair of vertices is contained in at least ( 1 / 3 + ε ) n edges contains a copy of C 10 , i.e. the tight cycle on 10 vertices. In fact we obtain the same conclusion for every cycle C ℓ with ℓ ≥ 19 .