Aleksandrov, A. G.; Zuo, H.-Q. Zero-dimensional gradient singularities. (English) Zbl 1380.32031 Methods Appl. Anal. 24, No. 2, 169-184 (2017). Summary: We discuss an approach to the problem of classifying zero-dimensional gradient quasihomogeneous singularities using simple properties of deformation theory. As an example, we enumerate all such singularities with modularity \(\mathscr{P} = 0\) and with Milnor number not greater than \(12\). We also compute normal forms and monomial vector-bases of the first cotangent homology and cohomology modules, the corresponding Poincaré polynomials, inner modality, inner modularity, primitive ideals, etc. MSC: 32S25 Complex surface and hypersurface singularities 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14F40 de Rham cohomology and algebraic geometry 58K45 Singularities of vector fields, topological aspects 58K70 Symmetries, equivariance on manifolds Keywords:gradient singularities; deformation; cotangent homology and cohomology PDFBibTeX XMLCite \textit{A. G. Aleksandrov} and \textit{H. Q. Zuo}, Methods Appl. Anal. 24, No. 2, 169--184 (2017; Zbl 1380.32031) Full Text: DOI