{"id":878,"date":"2024-03-29T10:23:29","date_gmt":"2024-03-29T17:23:29","guid":{"rendered":"\/wp\/hades\/?p=878"},"modified":"2024-03-29T10:23:29","modified_gmt":"2024-03-29T17:23:29","slug":"the-sign-of-scalar-curvature-on-kahler-blowups","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/03\/29\/the-sign-of-scalar-curvature-on-kahler-blowups\/","title":{"rendered":"The Sign of Scalar Curvature on K\u00e4hler Blowups"},"content":{"rendered":"\n\t\t\t\t\n<p class=\"wp-block-paragraph\"> The HADES seminar on Tuesday,&nbsp;<strong>April 2nd<\/strong>, will be at <strong>3:30pm<\/strong>&nbsp;in&nbsp;<strong>Room 939.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Speaker: <\/strong><a href=\"https:\/\/math.berkeley.edu\/~gmbrown\/\">Garrett Brown<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract: <\/strong> Blowing up is a construction in complex geometry that can be thought of as the analog to connected sum in smooth topology. In this talk we will show that the property of having a positive (or negative) scalar curvature K\u00e4hler metric is preserved under blowing up points on a compact complex manifold of any dimension. This is done by solving a certain prescribed scalar curvature equation. The most crucial step is establishing uniform estimates for the linearized scalar curvature operators of a family of metrics on the blowup, for which the underlying geometry plays an interesting role. In the case of positive scalar curvature in two complex dimensions, this answers a question of Hitchin and Lebrun in the affirmative and completes the classification of positive scalar curvature K\u00e4hler surfaces. <\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,&nbsp;April 2nd, will be at 3:30pm&nbsp;in&nbsp;Room 939. Speaker: Garrett Brown Abstract: Blowing up is a construction in complex geometry that can be thought of as the analog to connected sum in smooth topology. In this talk we will show that the property of having a positive (or negative) scalar curvature K\u00e4hler [&hellip;]<\/p>\n","protected":false},"author":87,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-878","post","type-post","status-publish","format-standard","hentry","category-spring-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/878","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/87"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=878"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/878\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}