THE SAITO VECTOR FIELD OF A GERM OF COMPLEX PLANE CURVE.

The paper proves, via a combinatorial Saito-dicriticity on the ordered, numbered resolution tree, semi-local model gluing, and a weakly equisingular deformation argument, that the colored, numbered tree of a Saito vector field is a topological invariant for generic curves. The model gives a different, local-and-inductive proof strategy: (i) color exceptional components using whether the blow-up center is singular (white) or a smooth point of a single component (black), and (ii) count singularities on a component as corners with white neighbors plus arrowheads, excluding other zeros generically using local normal forms for Der(log Δ). The paper’s argument is complete; the model’s is largely correct but takes existence and genericity of Saito fields as given and compresses several technical steps (e.g., generic avoidance of extra zeros and the deformation-to-generic argument).