For a regular homogeneous polynomial f of degree m in n variables, any g = f + terms of order at least n(m-2)+1 defines a germ analytically isomorphic to {f=0}.
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A remark on isolated complex hypersurface singularities
For a regular homogeneous polynomial f of degree m in n variables, any g = f + terms of order at least n(m-2)+1 defines a germ analytically isomorphic to {f=0}.