Vol. 93, No. 2, 1981

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Differentiably k-normal analytic spaces and extensions of holomorphic differential forms

Lawrence James Brenton

Vol. 93 (1981), No. 2, 261–268

In this paper the concept of normality for a complex analytic space X is strengthened to the requirement that every local holomorphic p-form, for all 0 p  some integer k, defined on the regular points of X extend across the singular variety. A condition for when this occurs is given in terms of a notion of independence, in the exterior algebra ΩΔN, of the differentials dF1,,dFr of local generating functions Fi of the ideal of X in some ambient polydisc ΔN CN. One result is that for a complete intersection, “k-independent implies (k 2)-normal” (precise definitions are given below), which extends some ideas of Oka, Abhyankar, Thimm, and Markoe on criteria for normality.

Mathematical Subject Classification 2000
Primary: 32C40, 32C40
Secondary: 32C36
Received: 22 May 1979
Revised: 18 March 1980
Published: 1 April 1981
Lawrence James Brenton