The invention relates to an assembly for a turbine engine extending about a longitudinal axis, comprising: a nose cone (20) comprising a conical body (22) extending about the longitudinal axis and a flange (23) comprising a first contact surface (24) forming an extension of an inner surface (25) of the conical body (22); a front shroud (21) comprising an overall annular body (26) extending about the longitudinal axis and a flange (27) comprising a first contact surface (28) forming an extension of an outer surface (29) of the annular body (26), the first contact surface (24) of the nose cone (20) being in contact with the first contact surface (28) of the front shroud (21), the first contact surfaces (24, 28) of the nose cone (20) and the front shroud (21) being tilted in the downstream direction towards the longitudinal axis, so that the flange (23) of the nose cone (20) is secured to the flange (27) of the front shroud (21); and attachment elements (30) configured to clamp the first contact surface (24) of the flange (23) of the nose cone (20) against the first contact surface (28) of the flange (27) of the front shroud (21).