Purity of critical cohomology and Kac's conjecture
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 (Q,W) associated to Q, which in turn implies positivity of the Kac polynomials for Q.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.