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 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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- June 2003
- DOI:
- 10.48550/arXiv.math/0306369
- arXiv:
- arXiv:math/0306369
- Bibcode:
- 2003math......6369H
- Keywords:
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- Algebraic Geometry;
- Combinatorics;
- Differential Geometry
- E-Print:
- Latex, 7 pages