Algebra Seminar

A moduli algebra of an islated hypersurface singularity defined by f in Cⁿ is a finite dimensional C-algebra C{z₁,...,z_n} quotient by the ideal generated by f and its first partial derivatives. Mather and Yau proved that two germs of complex analytic hypersurfaces of the same dimension with isolated singularities are biholomorphically equivalent if and only if their moduli algebras are isomorphic. This means that we should be able to determine the singularity by means of studying its corresponding commutative Artinian local algebra. We shall give algebraic determination of isomorphism classes of the moduli algebras of simple elliptic singularites.