{"id":1516,"date":"2023-05-30T14:45:38","date_gmt":"2023-05-30T06:45:38","guid":{"rendered":"https:\/\/blog.vanabel.cn\/?p=1516"},"modified":"2023-05-30T14:45:38","modified_gmt":"2023-05-30T06:45:38","slug":"asymptotic-behaviour-of-the-hitchin-metric-on-the-moduli-space-of-higgs-bundles","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1516","title":{"rendered":"Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles"},"content":{"rendered":"<p>Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles<\/p>\n<p>Takuro Mochizuki<br \/>\nThe moduli space of stable Higgs bundles of degree 0 is equipped with the hyperk\u00e4hler metric, called the Hitchin metric. On the locus where the Hitchin fibration is smooth, there is the hyperk\u00e4hler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray (E,t\u03b8) as t\u2192\u221e.<br \/>\nSubjects:\tDifferential Geometry (math.DG); Algebraic Geometry (math.AG)<br \/>\nMSC classes:\t53C07, 58E15, 14D21, 81T13<br \/>\nCite as:\tarXiv:2305.17638 [math.DG]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Asymptotic behaviour of the Hitchin metric on the modul&hellip; <a class=\"more-link\" href=\"https:\/\/blog.vanabel.cn\/?p=1516\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[248],"tags":[272,271,273],"class_list":["post-1516","post","type-post","status-publish","format-standard","hentry","category-arxiv","tag-higgs","tag-hitchin","tag-hyperkahler","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1516","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1516"}],"version-history":[{"count":1,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1516\/revisions"}],"predecessor-version":[{"id":1517,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1516\/revisions\/1517"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1516"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1516"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1516"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}