= Torsion trivialization in a determinant quotient
Evaluation <determinants> for $L\otimes P$ and $L$ have a quotient which is a rational section of $\bigotimes_i\operatorname{pr}_i^*P$, not intrinsically a scalar. If $P^N\cong\mathcal O_C$, its $N$th power becomes a <rational function> after choosing that trivialization. In <Cartier divisor> notation, write $P=\mathcal O_C(p)$ and $\operatorname{div}(h)=Np$. With raw meromorphic evaluations the scalar expression is $r^N\prod_i h(z_i)$. The extra product accounts for the line-bundle frames; it is suppressed when evaluation already uses compatible torsion trivializations.
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