Complete Coordinate-free Characterization of Isolated Homogeneous Singularities and Derivations of the Moduli

Three main topics are stated in this thesis. The first topic is about complete characterization of homogeneous isolated hypersurface singularities which will be considered in Chapter 3. The second topic is about Haperin conjecture in singularity theory which will be considered in Chapter 4. The third topic is about characterization of isolated complete intersection singularities with C*action of dimension n>1 by means of geometric genus and irregularity which will be considered in Chapter 5.