Instanton sheaves on complex projective spaces

TL;DR

This paper investigates a class of torsion-free sheaves on complex projective spaces, generalizing instanton bundles, and explores their stability, cohomological properties, and moduli spaces.

Contribution

It introduces a broader class of instanton sheaves via monads, analyzes their semistability, and studies their moduli spaces.

Findings

Instanton sheaves are semistable when rank is not too large.

Certain cohomological conditions characterize instanton sheaves.

Examples of moduli spaces of instanton sheaves are provided.

Abstract

We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of moduli spaces of instanton sheaves.