A new non-reduced moduli component of rank 2 semistable sheaves on P3

TL;DR

This paper introduces a new, generically non-reduced component of the moduli space of rank-2 semistable sheaves on P3 with specific Chern classes, expanding understanding of the moduli space's structure.

Contribution

It constructs a novel non-reduced component of the Gieseker-Maruyama moduli space using elementary transformations and Mumford's example, revealing complex geometric structures.

Findings

Identifies a new non-reduced component in the moduli space

Uses elementary transformations to construct the component

Connects the component to Mumford's example of space curves

Abstract

In the present paper we describe new component of the Gieseker-Maruyama moduli space $\mathcal{M}(14)$ of coherent semistable rank-2 sheaves with Chern classes $c_1=0, \ c_2=14, \ c_3=0$ on $\mathbb{P}^{3}$ which is generically non-reduced. The construction of this component is based on the technique of elementary transformations of sheaves and famous Mumford's example of a non-reduced component of the Hilbert scheme of smooth space curves of degree 14 and genus 24.