Intersection forms of toric hyperkähler varieties

Hausel, Tamás; Swartz, Edward

doi:10.1090/S0002-9939-06-08248-7

Intersection forms of toric hyperkähler varieties
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by Tamás Hausel and Edward Swartz PDF

Proc. Amer. Math. Soc. 134 (2006), 2403-2409 Request permission

Abstract:

This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial $L^2$ harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of $L^2$ harmonic forms on complete hyperkähler manifolds of linear growth.

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