L2-Cohomology of quasi-fibered boundary metrics

• 成果类型: Article
• 署名作者: Kottke, Chris; Rochon, Frederic
• 署名单位: State University System of Florida; New College Florida; University of Quebec; University of Quebec Montreal
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01253-5
• 发表日期: 2024
• 页码: 1083-1131
• 关键词: hodge cohomology; MANIFOLDS; Operators; PRODUCTS; geometry; SPACE

摘要

We develop new techniques to compute the weighted L-2-cohomology of quasi-fibered boundary metrics (QFB-metrics). Combined with the decay of L-2-harmonic forms obtained in a companion paper, this allows us to compute the reduced L-2-cohomology for various classes of QFB-metrics. Our results applies in particular to the Nakajima metric on the Hilbert scheme of n points on C-2 , for which we can show that the Vafa-Witten conjecture holds. Using the compactification of the monopole moduli space announced by Fritzsch, the first author and Singer, we can also give a proof of the Sen conjecture for the monopole moduli space of magnetic charge 3.