Intersection forms of toric hyperkaehler varieties

Details Intersection forms of toric hyperkaehler varieties Intersection forms of toric hyperkaehler varieties

2003-06-25

arxiv.org/abs/math/0306369v1

Mathematics

Algebraic Geometry

Latex, 7 pages

Scientific paper

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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