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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A rank theorem for coherent analytic sheaves


Author: Günther Trautmann
Journal: Trans. Amer. Math. Soc. 157 (1971), 495-498
MSC: Primary 32.50
MathSciNet review: 0276498
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Abstract: Let $ S$ be an analytic subvariety in $ {C^n}$ and $ \mathcal{F}$ a coherent analytic sheaf on $ {C^n}$, such that $ \mathcal{F}$ is locally free on $ {C^n} - S$ and $ \Gamma (U,\mathcal{F}) = \Gamma (U - S,\mathcal{F})$ for every open set $ U \subset {C^n}$. It is shown that $ \mathcal{F}$ is locally free everywhere, if codh$ \mathcal{F} \geqq n - 1$ and $ \dim S +$   rank$ \mathcal{F} \leqq n - 2$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0276498-5
Keywords: Coherent analytic sheaves, homological codimension, rank, resolutions of ideals
Article copyright: © Copyright 1971 American Mathematical Society