Stratifications for moduli of sheaves and moduli of quiver representations

2014/07/15 by Hoskins, Victoria · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.4057

Abstract

We study the relationship between two stratifications on parameter spaces for coherent sheaves and for quiver representations: a stratification by Harder-Narasimhan types and a stratification arising from the geometric invariant theory construction of the associated moduli spaces of semistable objects. For quiver representations, both stratifications coincide, but this is not quite true for sheaves. We explain why the stratifications on various Quot schemes do not coincide and see that the correct parameter space to compare such stratifications is the stack of coherent sheaves. Then we relate these stratifications for sheaves and quiver representations using a generalisation of a construction of Álvarez-Cónsul and King.

Cited by

• Harder-Narasimhan filtrations of decorated vector bundles
• Harder-Narasimhan Filtration on Moment Map for Quiver Representations
• The QuiverTools package for SageMath and Julia

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