2024/10/20 by Panagiotis Dimakis, Dimakis, Panagiotis, Frédéric Rochon +1 · 2 citations
Mathematics · #53C26 #53D20 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2410.15424
openalex publication_date 2024/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using an approach developed by Melrose to study the geometry at infinity of the Nakajima metric on the reduced Hilbert scheme of points on ℂ2, we show that the Nakajima metric on a quiver variety is quasi-asymptotically conical (QAC) whenever its defining parameters satisfy an appropriate genericity assumption. As such, it is of bounded geometry and of maximal volume growth. Being QAC is one of two main ingredients allowing us to use the work of Kottke and the second author to compute its reduced L2-cohomology and prove the Vafa-Witten conjecture. The other is a vanishing theorem in L2-cohomology for exact wedge 3-Sasakian metrics generalizing a result of Galicki and Salamon for closed 3-Sasakian manifolds.