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Donaldson-Thomas invariants versus intersection cohomology of quiver moduli

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arxiv 1411.4062 v2 pith:QLQMVXWV submitted 2014-11-14 math.AG math.RT

classification math.AGmath.RT
keywords donaldson-thomasintersectionquiverresultcohomologyconjectureintegralitymain
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The main result of this paper is the statement that the Hodge theoretic Donaldson-Thomas invariant for a quiver with zero potential and a generic 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 relating the Donaldson-Thomas "function" to the intersection complex. The proof of our main result relies on a relative version of the integrality conjecture in Donaldson-Thomas theory. This will be the topic of the second part of the paper, where the relative integrality conjecture will be proven in the motivic context.

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  1. Wild wall-crossing and symmetric quivers in 4d and 3d $\mathcal{N}=2$ field theories

    hep-th 2025-06 conditional novelty 6.0 of 10

    The paper derives a tree-of-unlinkings formula for wild Donaldson-Thomas invariants of m-Kronecker quivers from wall-crossing identities rewritten through symmetric quivers and diagonalization.

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