Parallels between moduli of quiver representations and vector bundles over curves
| Autor: | Victoria Hoskins |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
010308 nuclear & particles physics 010102 general mathematics Quiver Mathematics::Rings and Algebras Vector bundle 01 natural sciences Cohomology Moduli space Moduli Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics Geometry and Topology Geometric invariant theory 0101 mathematics Mathematics::Representation Theory Moment map Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematical Physics Analysis Mathematics Symplectic geometry |
| Popis: | This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their moduli spaces via geometric invariant theory and symplectic reduction, we introduce their hyperk\"ahler analogues: moduli spaces of representations of a doubled quiver satisfying certain relations imposed by a moment map and moduli spaces of Higgs bundles. Finally, we survey a surprising link between the counts of absolutely indecomposable objects over finite fields and the Betti cohomology of these (complex) hyperk\"ahler moduli spaces due to work of Crawley-Boevey and Van den Bergh and Hausel, Letellier and Rodriguez-Villegas in the quiver setting, and work of Schiffmann in the bundle setting. |
| Databáze: | OpenAIRE |
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