{"status":"public","publication":"Proceedings of the American Mathematical Society","oa":1,"type":"journal_article","_id":"1461","day":"01","month":"08","date_published":"2006-08-01T00:00:00Z","citation":{"chicago":"Hausel, Tamas, and Edward Swartz. “Intersection Forms of Toric Hyperkähler Varieties.” *Proceedings of the American Mathematical Society* 134, no. 8 (2006): 2403–9. https://doi.org/10.1090/S0002-9939-06-08248-7.","apa":"Hausel, T., & Swartz, E. (2006). Intersection forms of toric hyperkähler varieties. *Proceedings of the American Mathematical Society*, *134*(8), 2403–2409. https://doi.org/10.1090/S0002-9939-06-08248-7","ieee":"T. Hausel and E. Swartz, “Intersection forms of toric hyperkähler varieties,” *Proceedings of the American Mathematical Society*, vol. 134, no. 8, pp. 2403–2409, 2006.","ista":"Hausel T, Swartz E. 2006. Intersection forms of toric hyperkähler varieties. Proceedings of the American Mathematical Society. 134(8), 2403–2409.","mla":"Hausel, Tamas, and Edward Swartz. “Intersection Forms of Toric Hyperkähler Varieties.” *Proceedings of the American Mathematical Society*, vol. 134, no. 8, American Mathematical Society, 2006, pp. 2403–09, doi:10.1090/S0002-9939-06-08248-7.","ama":"Hausel T, Swartz E. Intersection forms of toric hyperkähler varieties. *Proceedings of the American Mathematical Society*. 2006;134(8):2403-2409. doi:10.1090/S0002-9939-06-08248-7","short":"T. Hausel, E. Swartz, Proceedings of the American Mathematical Society 134 (2006) 2403–2409."},"author":[{"full_name":"Tamas Hausel","first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"first_name":"Edward","full_name":"Swartz, Edward","last_name":"Swartz"}],"quality_controlled":0,"publication_status":"published","date_created":"2018-12-11T11:52:09Z","page":"2403 - 2409","issue":"8","doi":"10.1090/S0002-9939-06-08248-7","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/0306369"}],"publisher":"American Mathematical Society","publist_id":"5733","volume":134,"intvolume":" 134","date_updated":"2019-04-26T07:22:03Z","year":"2006","extern":1,"abstract":[{"lang":"eng","text":"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."}],"title":"Intersection forms of toric hyperkähler varieties","acknowledgement":"The first author was partly supported by NSF grant DMS-0072675. The second author was partly supported by a VIGRE postdoc under NSF grant number 9983660 to Cornell University."}