Vector fields and admissible embeddings for quiver moduli

Abstract

We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal representation, to computations involving line bundles, making them amenable to methods from geometric invariant theory. We will use this to show that in many good situations the vector fields on the moduli space are isomorphic as a vector space to the first Hochschild cohomology of the path algebra. We also show that considering the universal representation as a Fourier-Mukai kernel in the appropriate sense gives an admissible embedding of derived categories.

arXiv commentv2: added references, 23 pages, all comments welcome

References in corpus (6)

• The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli
• Derived categories of curves as components of Fano manifolds
• Derived categories of (nested) Hilbert schemes
• Hilbert squares: derived categories and deformations
• Admissible subcategories in derived categories of moduli of vector bundles on curves
• Fano quiver moduli