Lazarsfeld-Mukai Reflexive Sheaves and their Stability

Abstract

Consider an ample and globally generated line bundle $L$ on a smooth projective variety $X$ of dimension $N\ge 2$ over $\mathbb{C}$. 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 ${\mu }_L$-(semi)stability of such reflexive sheaves under certain conditions.

12 pages, Revised version, Accepted for publication in Communications in Algebra