2005/09/23 by Imre Patyi, Patyi, Imre
Mathematics · #32L20 #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32L20
paper · pdf · doi:10.48550/arxiv.math/0509556
14 pages
arxiv created 2005/09/23 · openalex publication_date 2005/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the holomorphic ideal sheaf of a linear section of a pseudoconvex open subset Ω of, say, a Hilbert space X=ℓ2 is acyclic. We also prove an analog of Hefer's lemma, i.e., if f:Ω×Ω→\CC is holomorphic and f(x,x)=0 for x∈Ω, then there is a holomorphic g:Ω×Ω→ X^* with values in the dual space X^* of X such that f(x,y)=g(x,y)(x-y)