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Donaldson–Thomas invariants versus intersection cohomology of quiver moduli

  • Sven Meinhardt EMAIL logo and Markus Reineke

Abstract

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.

Acknowledgements

The main result of the paper was originally observed and conjectured by J. Manschot while doing some computations. The first author is very grateful to him for sharing his observations and his conjecture which was the starting point of this paper. The authors would also like to thank V. Ginzburg, E. Letellier, M. Kontsevich and L. Migliorini for interesting discussions on the results of this paper and Jörg Schürmann for answering patiently all questions about mixed Hodge modules.

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Received: 2016-01-13
Revised: 2016-11-14
Published Online: 2017-03-17
Published in Print: 2019-09-01

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