Application of classical invariant theory to biholomorphic classification of plane curve singularities, and associated binary forms (1106.2602v3)

Abstract: 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 way of extracting a complete set of invariants of homogeneous plane curve singularities from their moduli algebras.