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

Algebraic Geometry