Purity of critical cohomology and Kac's conjecture

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We provide a new proof of the Kac positivity conjecture for an arbitrary quiver Q. The ingredients are the cohomological integrality theorem in Donaldson–Thomas theory, dimensional reduction, and an easy purity result. These facts imply the purity of the cohomological Donaldson–Thomas invariants for partially nilpotent representations of a quiver with potential (Q˜,W) associated to Q, which in turn implies positivity of the Kac polynomials for Q.
Original languageEnglish
Article number2
Pages (from-to)469-488
Number of pages19
JournalMathematical research letters
Issue number2
Publication statusPublished - 5 Jul 2018


  • Kac polynomials
  • purity
  • positivity


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