Lazarsfeld-Mukai Reflexive Sheaves and their Stability

2017/05/09 by Narayanan, Poornapushkala
#14C20 #14J60 #14M10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.03171

Abstract

Consider an ample and globally generated line bundle L on a smooth projective variety X of dimension N≥ 2 over ℂ. Let D be a smooth divisor in the complete linear system of L. We construct reflexive sheaves on X by an elementary transformation of a trivial bundle on X along certain globally generated torsion-free sheaves on D. The dual reflexive sheaves are called the Lazarsfeld-Mukai reflexive sheaves. We prove the μ_L-(semi)stability of such reflexive sheaves under certain conditions.

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