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

2023/03/23 by Rekuski, Nick
#14D20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.13459

Abstract

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.

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