Reflexive and spanned sheaves on $\mathbb{P}^3$

TL;DR

This paper studies reflexive sheaves on projective 3-space that are spanned in codimension 2 with low first Chern class, providing conditions for indecomposability and showing all such sheaves with c1=2 are spanned.

Contribution

It offers new criteria for the indecomposability of reflexive sheaves on P^3 and characterizes when these sheaves are spanned, especially for low c1 values.

Findings

Characterization of reflexive sheaves spanned in codimension 2 on P^3.

Necessary and sufficient conditions for indecomposability.

Proof that all reflexive sheaves with c1=2 are spanned.

Abstract

We investigate the reflexive sheaves on $\PP^3$ spanned in codimension 2 with very low first Chern class $c_1$. We also give the sufficient and necessary conditions on numeric data of such sheaves for indecomposabiity. As a by-product we obtain that every reflexive sheaf on $\PP^3$ spanned in codimension 2 with $c_1=2$ is spanned.