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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
Posted:
February 6, 2006
MathSciNet review:
2213714
Full-text PDF Free Access
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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  harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of  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
Posted:
February 6, 2006
Communicated by:
Michael Stillman
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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