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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Intersection forms of toric hyperkähler varieties


Authors: Tamás Hausel and Edward Swartz
Journal: Proc. Amer. Math. Soc. 134 (2006), 2403-2409
MSC (2000): Primary 53C26; Secondary 52C35
Published electronically: February 6, 2006
MathSciNet review: 2213714
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Abstract: 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.


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Additional Information

Tamás Hausel
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1082
Email: hausel@math.utexas.edu

Edward Swartz
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Email: ebs@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08248-7
PII: S 0002-9939(06)08248-7
Received by editor(s): June 21, 2004
Received by editor(s) in revised form: March 9, 2005
Published electronically: February 6, 2006
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.