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We show the kernel sheaf associated to a sufficiently positive torsion-freesheaf of rank 1 is slope stable. Furthermore, we are able to give an explicitbound for "sufficiently positive." This settles a conjecture ofEin-Lazarsfeld-Mustopa. The main technical lemma is a bound on the number ofglobal sections of a torsion-free, globally generated sheaf in terms of itsrank, degree, and invariants of the variety.

Stability of Kernel Sheaves Associated to Rank One Torsion-Free Sheaves