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We study the Jacobian scheme of a plane algebraic curve at an ordinary singularity, characterizing it through a geometric property. We give an algorithm that gives the analytic type of a double point using the algebraic version of the Mather-Yau Theorem. We give a characterization of plane nodal curves with no infinitely near points through their Tjurina number.
Canino et al. (Thu,) studied this question.
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