= Additivity of analytic divisor line bundles
{title2=$[D_1+D_2]\cong[D_1]\otimes[D_2]$}
If $f_i$ and $g_i$ are local meromorphic equations for two <divisors on a complex manifold>, then $f_ig_i$ defines their sum. With local frames satisfying $e_j=(f_i/f_j)e_i$, the <transition functions of a vector bundle> for the tensor product are the products of the two ratios, exactly those for $f_ig_i$. Multiplication of local frames therefore gives the displayed <holomorphic line bundle> isomorphism.
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