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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.

8 votes
2 answers
1k views

Is a torsion free sheave of rank one on a reducible curve the pushforward of a line bundle o...

Let $X$ be a nodal curve, possibly reducible. Then can any torsion free sheaf of rank one on $X$ be expressed as $\pi_*(L)$, where $L$ is a line bundle on a partial normalization of $X$? This looks st …