We investigate the magnetization of HgBa 2CuO 4+δ below the superconducting transition temperature (T c) using angle-dependent torque magnetometry. The anisotropy of the superconducting parameter γ is analyzed with the Kogan model. For underdoped samples, we observe significant temperature and field dependences in the temperature range of about 5-10K below T c. For an overdoped sample, the field and temperature dependences of γ are less significant. Our data at all doping levels are consistent with the possibility that, at fixed magnetic field strength, γ approaches a constant value at low temperature. The strong temperature dependence in the range 5-10K below T c in the underdoped samples might arise from enhanced fluctuations due to the much larger anisotropy than in the overdoped case. At temperatures close to T c, γ is dramatically reduced due to the breakdown of the Kogan model as a result of critical fluctuations combined with the non-zero superconducting transition width of the samples.