Say you have [tex]exp{(\omega)}[/tex] and [tex]\omega[/tex] has a simple pole show that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]exp{(\omega)}=exp{(F+)}z^{-1}exp{(F-)}[/tex] where F+ is holomorphic and F- is antiholomorphic. My basic thought is if [tex]\omega[/tex] has a simple pole then [tex]\omega z[/tex] is holomorphic and on the punctured disk it can be represented by a Laurant series. The problem is that I'm missing a factor of log on z.

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# Grothendieck decompostion simple example

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