Let $k$ be an infinite field, $X$ a smooth, projective curve over $k$ and $F$ a pure, coherent sheaf on $X$. Let $F'$ be the maximal destabilizing sheaf of $F$. Is the quotient sheaf $F/F'$ locally free?
Is quotient by maximal destabilizing sheaf, torsion-free?
user45397
- 2.3k
- 13
- 24