Sheaves of low rank in three dimensional projective space

TL;DR

This paper classifies semistable sheaves of rank up to four in three-dimensional projective space and demonstrates that their moduli spaces are smooth and irreducible when the third Chern character is maximal.

Contribution

It provides a classification of Chern characters for low-rank semistable sheaves and establishes smoothness and irreducibility of their moduli spaces in specific cases.

Findings

Classification of Chern characters up to rank four

Moduli spaces are smooth and irreducible for maximal third Chern character

Results apply to semistable sheaves in three-dimensional projective space

Abstract

We classify Chern characters of semistable sheaves up to rank four in three dimensional projective space. As a corollary we show that moduli spaces of semistable sheaves between rank zero and four with maximal third Chern character are smooth and irreducible.