Vol. 47, No. 1, 1973

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The weak envelope of holomorphy for algebras of holomorphic functions

Alan Trinler Huckleberry

Vol. 47 (1973), No. 1, 115–128

The object of this paper is to study analytic continuation of algebras of functions holomorphic on complex spaces of dimension greater than 1. Classically this has been done by putting complex structure on the maximal spectrum of the algebra so that the spectrum is a Stein space with respect to the induced algebra of holomorphic functions. Grauert has given non-pathological examples where this is not possible. In the present paper the axioms of a Stein space have been weakened and the weak envelope of holomorphy has been constructed for a certain type of algebra. In particular, if the algebra A separates points and gives local coordinates on a complex space X then the weak envelope of holomorphy for the pair, (X,A) is obtained.

Mathematical Subject Classification 2000
Primary: 32D10
Received: 30 March 1972
Published: 1 July 1973
Alan Trinler Huckleberry