
School of Mathematics and Statistics
Stephen Yau
University of Illinois at Chicago
Algebraic determination of isomorphism classes of the moduli
algebras of simple elliptic singularities.
Wednesday 13th December, 34pm, Carslaw 275.
A moduli algebra of an islated hypersurface singularity defined by
f in C^{n} is a finite dimensional
Calgebra C{z_{1},...,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.
