Purity of critical cohomology and Kac's conjecture

10 Mar 2017 · Davison Ben ·

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 a quiver with potential $(\tilde{Q},W)$ associated to $Q$, which in turn implies positivity of the Kac polynomials for $Q$.

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Purity of critical cohomology and Kac's conjecture

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