Moduli Spaces of Unstable Objects: Sheaves of Harder-Narasimhan Length 2
Algebraic Geometry
2021-11-16 v1
Abstract
Given a moduli problem posed using Geometric Invariant Theory, one can use Non-Reductive Geometric Invariant Theory to quotient unstable HKKN strata and construct 'moduli spaces of unstable objects', extending the usual moduli classifications. After giving a self-contained account of how to do this, we apply this method to construct moduli spaces for certain unstable coherent sheaves of HN length 2 on a projective scheme, which we call -stable sheaves. This extends a previous result of Brambila-Paz and Mata-Guti\'{e}rrez for rank two vector bundles on a curve.
Keywords
Cite
@article{arxiv.2111.07428,
title = {Moduli Spaces of Unstable Objects: Sheaves of Harder-Narasimhan Length 2},
author = {Joshua Jackson},
journal= {arXiv preprint arXiv:2111.07428},
year = {2021}
}