= Conormal line of a smooth analytic hypersurface
{title2=$[-Y]|_Y\cong N^*_{Y/X}$}
For reduced local equations $f_j=u_{ji}f_i$ with $u_{ji}$ a holomorphic unit, the <holomorphic line bundle associated to a divisor> $[-Y]$ has local generators $f_i$ and transition $u_{ji}$. Differentiation along $Y$ gives $df_j|_Y=u_{ji}|_Y\,df_i|_Y$. Sending the restricted local generator to $df_i|_Y$ gives the conormal isomorphism. The term $f_i\,du_{ji}$ disappears only after restricting to $Y$.
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