A complex line bundle is a vector bundle 
whose fibers 
are a copy of 
. 
is a holomorphic line bundle if it is a holomorphic
map between complex manifolds and its transition functions are holomorphic.
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On a compact Riemann surface, a variety divisor 
determines a line bundle. For example, consider 
on 
. Around 
there is a coordinate chart 
given by the holomorphic
function 
with 
.
Similarly, 
is a holomorphic function defining a disjoint
chart 
around 
with 
.
Then letting 
,
the Riemann surface is covered by 
. The line bundle
corresponding to 
is then defined by the following transition
functions,
 |  |  |
(1)
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(2)
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