2003/06/25 by Tamás Hausel, Tamas Hausel, Hausel, Tamas +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.CO #math.DG
paper · pdf · doi:10.48550/arxiv.math/0306369
Latex, 7 pages
arxiv created 2003/06/25 · openalex publication_date 2003/06/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note proves combinatorially that the intersection pairing on the middle dimensional compactly supported cohomology of a smooth toric hyperkaehler variety is always definite, providing a large number of non-trivial L2 harmonic forms for toric hyperkaehler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L2 harmonic forms on complete hyperkaehler manifolds of linear growth.