Algebraic singularities have maximal reductive automorphism groups

Abstract

Let X = On/i be an analytic singularity where ṫ is an ideal of the C-algebra On of germs of analytic functions on (Cn, 0). Let denote the maximal ideal of X and A = Aut X its group of automorphisms. An abstract subgroup equipped with the structure of an algebraic group is called algebraic subgroup of A if the natural representations of G on all “higher cotangent spaces” are rational. Let π be the representation of A on the first cotangent space and A1 = π(A).