Geodesic
Application of classical invariant theory to biholomorphic classification of plane curve singularities, and associated binary forms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 257-268

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We use classical invariant theory to solve the biholomorphic equivalence problem for two families of plane curve singularities previously considered in the literature. Our calculations motivate an intriguing conjecture that proposes a method for extracting a complete set of invariants of homogeneous plane curve singularities from their moduli algebras. 
@article{TM_2012_279_a16,
     author = {A. V. Isaev},
     title = {Application of classical invariant theory to biholomorphic classification of plane curve singularities, and associated binary forms},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {257--268},
     publisher = {mathdoc},
     volume = {279},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_279_a16/}
}
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A. V. Isaev. Application of classical invariant theory to biholomorphic classification of plane curve singularities, and associated binary forms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 257-268. http://geodesic.mathdoc.fr/item/TM_2012_279_a16/