Quotients of unstable subvarieties and moduli spaces of sheaves of fixed Harder-Narasimhan type

Abstract

When a reductive group $G$ acts linearly on a complex projective scheme $X$ there is a stratification of $X$ into $G$-invariant locally closed subschemes, with an open stratum $X^{ss}$ formed by the semistable points in the sense of Mumford's geometric invariant theory which has a categorical quotient $X^{ss}\to X//G$. In this article we describe a method for constructing quotients of the unstable strata. As an application, we construct moduli spaces of sheaves of fixed Harder-Narasimhan type with some extra data (an '$n$-rigidification') on a projective base.

33 pages, minor revision. To appear in the Proceedings of the London Mathematical Society

References in corpus (1)

• A functorial construction of moduli of sheaves

Cited by in corpus (4)

• On the structure of instability in moduli theory
• Stratifications on the Moduli Space of Higgs Bundles
• A GIT interpretration of the Harder-Narasimhan filtration
• Moduli Spaces of Unstable Objects: Sheaves of Harder-Narasimhan Length 2