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

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

2011-03-24

arxiv.org/abs/1103.4731v3

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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