Intersection forms of toric hyperkaehler varieties
Abstract
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.
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