[{"date_updated":"2021-01-12T06:50:54Z","_id":"1461","date_created":"2018-12-11T11:52:09Z","status":"public","publisher":"American Mathematical Society","publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/math/0306369","open_access":"1"}],"intvolume":" 134","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.","page":"2403 - 2409","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."}],"year":"2006","date_published":"2006-08-01T00:00:00Z","publication":"Proceedings of the American Mathematical Society","title":"Intersection forms of toric hyperkähler varieties","citation":{"ista":"Hausel T, Swartz E. 2006. Intersection forms of toric hyperkähler varieties. Proceedings of the American Mathematical Society. 134(8), 2403–2409.","chicago":"Hausel, Tamás, and Edward Swartz. “Intersection Forms of Toric Hyperkähler Varieties.” *Proceedings of the American Mathematical Society*. American Mathematical Society, 2006. 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. American Mathematical Society, pp. 2403–2409, 2006.","apa":"Hausel, T., & Swartz, E. (2006). Intersection forms of toric hyperkähler varieties. *Proceedings of the American Mathematical Society*. American Mathematical Society. https://doi.org/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.","mla":"Hausel, Tamás, 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."},"doi":"10.1090/S0002-9939-06-08248-7","oa":1,"type":"journal_article","volume":134,"publist_id":"5733","month":"08","quality_controlled":0,"issue":"8","day":"01","author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","first_name":"Tamas","last_name":"Hausel"},{"full_name":"Swartz, Edward","first_name":"Edward","last_name":"Swartz"}]}]