Suppose I have a stable, reducible, nodal curve with two components $C' \cup C''=C$ and two line bundles $L$ and $M$ on $C$. Suppose furthermore that $L^{\otimes r}=M$. What can I say about the restrictions $L'$ and $L''$ of $L$ to $C'$ and $C''$. Do we have $L_{C'}^{\otimes r}=M_{C'}$? I guess that the two bundles $L'$ and $L''$ should have some condition on the attaching point. (residue sum up to zero?)
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
