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Holomorphic Connections and Extension of Complex Vector Bundles

✍ Scribed by N. P. Buchdahl; Adam Harris

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
664 KB
Volume
204
Category
Article
ISSN
0025-584X

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✦ Synopsis

Let X 5 Y be a regular, surjective holomorphic map betnnen complex manifolds such that for rllt E Y, n-'(t) is a connected, simply connected Warnran surface. Let K C X be compact,

vector bundle, equipped with L holomorphic relative connection Jong the fibrea of R. T h e mdn result of this note eatablirhm unique SrirrtanCG of a holomorphic vector bundle extension & + X under the added rssumptions that x ( K ) b a proper subat of Y, md *'l(t) t l (X \ K) is J w a p non-empty m d connected. An L corollary of the mdn theorem, it follows that if X is m arbitmy complex maadfold, m d A c X b an mdytic subset of codimeneion r t lerst two, then E + X \ A admits L unique actemion if there e x W ~ L holomorphic connection v : b x ( E ) 4 n:,(E).

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