An assembly (50) for a turbine engine includes an annular row of stator blades with a longitudinal axis (B) having variable pitch blades each comprising a radial vane (6), at least one of its ends of which is connected to a radially extending pivot (14) and being engaged in rotation around its axis (A) in a ring (16), characterised in that a tubular component (26) is mounted coaxially around the pivot (14), wherein said tubular component (26) comprises a first annular zone (26a) mounted tightly on the pivot (14) and a second annular zone (26b) comprising an annular bulge (28) extending substantially radially outwards in relation to the axis (A) of the pivot (14), wherein the annular bulge (28) and the pivot (14) define an annular space (30).