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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.

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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