Suppose that $C$ is a compact Riemann surface o positive genus $g$. Let $L$ a linear bundle on $C$ .
Chosen a divisor $D$ on $C$ we consider the set $L(D)$ that is the tensor product between $L$ and the line bundle $[D]$: $L(D)=L \otimes[D] $
Does it make sense to define the quotien $L(D)/L$?
Due to the definition of $L$ i would say that $L(D)/L$ is trivial but i'm not sure.
The question arises because i'm reading Mumford's notes and i've found a commutative diagram that contains this.
Here the link (diagramm at page 183)
http://dash.harvard.edu/bitstream/handle/1/3612774/Mumford_ThetaCharAlgCurve.pdf?sequence=1