On strong Euler-homogeneity and Saito-holonomicity for complex hypersurfaces

Based on previous work on linear free divisors by Granger et al., we develop necessary and sufficient conditions for a general divisor to be strongly Euler-homogeneous in terms of some Fitting ideals. We also define the notions of weak and strong Saito-holonomicity for a general divisor in such a way that they extend the definitions of Saito-holonomicity and weak and strong Koszul-freeness. Then, we characterize these properties using the Fitting ideals previously defined. Finally, we generalize some results regarding Koszul-freeness and strong Euler-homogeneity to the non-free case.