Intersection forms of toric hyperkaehler varieties
Algebraic Geometry
2007-05-23 v1 Combinatorics
Differential Geometry
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 L^2 harmonic forms for toric hyperkaehler 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 hyperkaehler manifolds of linear growth.
Cite
@article{arxiv.math/0306369,
title = {Intersection forms of toric hyperkaehler varieties},
author = {Tamas Hausel and Edward Swartz},
journal= {arXiv preprint arXiv:math/0306369},
year = {2007}
}
Comments
Latex, 7 pages