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arXiv · 1311.6989

Purity of critical cohomology and Kac's conjecture

Ben Davison
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Abstract

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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Ben Davison. 2013-11-27. Purity of critical cohomology and Kac's conjecture. https://arxiv.org/abs/1311.6989

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