The method of conformal transformation is employed to extend the Van Hove Scenario (VHS) with regard to two-dimensional anisotropic superconductors. A new function, the kernel of the density of states (DOS) imposing a scalar field in the transformed energy-angle space is introduced and related to the standard DOS. The existence of singularities in the DOS can remarkably change thermodynamic properties of a superconductor. Some model singularities in the vicinity of the Fermi level (FL) resulting in both the increase and the decrease of the critical temperature are studied. The isotope effect and the suppression of superconductivity due to the singularities are also discussed.