Intersection forms of toric hyperkähler varieties

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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-08, Vol.134 (8), p.2403-2409
Main Authors: HAUSEL, Tamas, SWARTZ, Edward
Format: Article
Language:English
Subjects:
Algebra
Convex and discrete geometry
Differential geometry
Exact sciences and technology
Geometry
Hyperplanes
Magnetic monopoles
Mathematical manifolds
Mathematical theorems
Mathematics
Matroids
Quotients
Sciences and techniques of general use
String theory
Vertices
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-06-08248-7