2021/12/22 by Justin Sawon, Sawon, Justin
Mathematics · #53C26 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2112.11617
openalex publication_date 2021/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We conjecture that certain curvature invariants of compact hyperkähler manifolds are positive/negative. We prove the conjecture in complex dimension four, give an "experimental proof" in higher dimensions, and verify it for all known hyperkähler manifolds up to dimension eight. As an application, we show that our conjecture leads to a bound on the second Betti number in all dimensions.