ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 32 Tung, Chia-Chi, Mankato State University A Note on the Hilbert Nullstellen Satz The analytic Hilbert Nullstellen Satz is well-known: If the germ g_{a} at a in C^{m} of a holomorphic function g vanishes on the germ at a of the variety Z = {f_{1} = ⋯ = f_{N}}, then some power of g_{a} belongs to the ideal generated by the germs f_{j}_{,}_{a}. In this note this result is proved for holomophic functions defined on a normal complex space under suitable conditions, allowing the common zero set Z to be discrete or of positive dimension. It is also shown that the power for the germ g_{a} above is locally constant at every point of Z and is independent of g.