Sven Meinhardt, Markus Reineke
Published 2014-11-14Version 1
The paper has two aims. The main aim is to prove that the Hodge theoretic Donaldson-Thomas invariant for a quiver with zero potential and a generic King stability condition agrees with the compactly supported intersection cohomology of the closure of the stable locus inside the associated coarse moduli space of semistable quiver representations. In fact, we prove an even stronger result for the intersection complex. The second aim of the paper is to show that the integrality conjecture in Donaldson-Thomas theory holds for all abelian categories of homological dimension one. The result will be a direct consequence of a stronger version for Donaldson-Thomas "sheaves" on moduli spaces.
Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one
Projectivity and effective global generation of determinantal line bundles on quiver moduli
The decomposition theorem and the Intersection cohomology of the Satake-Baily-Borel compactification of ${\mathcal A}_g$ for small genus
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