Configurations in abelian categories. I. Basic properties and moduli stacks
| dc.creator | Joyce, Dominic | |
| dc.date | 2003-12-09 | |
| dc.date | 2006-03-15 | |
| dc.date.accessioned | 2026-07-07T06:35:51Z | |
| dc.date.available | 2026-07-07T06:35:51Z | |
| dc.description | This is the first in a series of papers math.AG/0503029, math.AG/0410267, math.AG/0410268 on "configurations" in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration (σ,ι,π) is a finite collection of objects σ(J) and morphisms ι(J,K) or π(J,K) : σ(J) --> σ(K) satisfying some axioms, where J,K are subsets of I. Configurations describe how an object X in A decomposes into subobjects, and are especially useful for studying stability conditions on A. This paper defines and motivates the idea of configurations, and explains some natural operations upon them -- subconfigurations, quotient configurations, refinements, improvements and substitution. Then we study moduli spaces of (I,<)-configurations in A, using the theory of Artin stacks. We prove well-behaved moduli stacks exist when A is an abelian category of coherent sheaves or vector bundles on a projective K-scheme P, or of representations of a quiver Q. We define many natural 1-morphisms between the moduli stacks, some of which are representable or of finite type. The sequels will apply these results to construct and study infinite-dimensional algebras associated to a quiver Q, and to define systems of invariants of a projective K-scheme P that "count" (semi)stable coherent sheaves and satisfy interesting identities. | |
| dc.description | 56 pages, LaTeX. (v6) Minor changes, now in final form | |
| dc.identifier | https://arxiv.org/abs/math/0312190 | |
| dc.identifier | http://arxiv.org/abs/math/0312190 | |
| dc.identifier | Advances in Mathematics 203 (2006), 194-255. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99920 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Category Theory | |
| dc.title | Configurations in abelian categories. I. Basic properties and moduli stacks | |
| dc.type | text |