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arXiv · 2111.07428

Moduli Spaces of Unstable Objects: Sheaves of Harder-Narasimhan Length 2

Joshua Jackson
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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 $\tau$-stable sheaves. This extends a previous result of Brambila-Paz and Mata-Guti\'{e}rrez for rank two vector bundles on a curve.

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Joshua Jackson. 2021-11-14. Moduli Spaces of Unstable Objects: Sheaves of Harder-Narasimhan Length 2. https://arxiv.org/abs/2111.07428

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