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Zero-dimensional gradient singularities. (English) Zbl 1380.32031

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
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