{"id":8179,"date":"2023-02-22T16:03:55","date_gmt":"2023-02-22T15:03:55","guid":{"rendered":"https:\/\/www.dm.unipi.it\/eventi\/tba-lars-halvard-halle-univerista-di-bologna\/"},"modified":"2023-03-22T18:37:26","modified_gmt":"2023-03-22T17:37:26","slug":"tba-lars-halvard-halle-univerista-di-bologna","status":"publish","type":"unipievents","link":"https:\/\/www.dm.unipi.it\/en\/eventi\/tba-lars-halvard-halle-univerista-di-bologna\/","title":{"rendered":"Degenerations of Hilbert schemes and relative VGIT &#8211; Lars Halvard Halle (Universit\u00e0 di Bologna)"},"content":{"rendered":"<h4>Venue<\/h4>\n<p>Department of Mathematics, Aula Magna.<\/p>\n<h4 class='mt-4'>Abstract<\/h4>\n<div style=\"background-color:white\"><span style=\"background-color:white\"><span style=\"font-size:12pt\">Let G be a reductive group acting on a projective variety X.&nbsp; In Mumford&#8217;s Geometric Invariant Theory (GIT),&nbsp; the formation of a quotient in this situation depends on the choice of a G-linearized ample line bundle on X. In &#8220;Variation of GIT&#8221; (VGIT), one studies various aspects of this dependence.&nbsp;<\/span><\/span><\/div>\n<div style=\"background-color:white\">\n<div>&nbsp;<\/div>\n<div><span style=\"background-color:white\"><span style=\"font-size:12pt\">I will report on joint work with K. Hulek and Z. Zhang, and explain how some central results in VGIT can be extended to a relative setting. Our main motivation was to apply these results to the study of certain Hilbert scheme degenerations constructed as relative GIT quotients. In the second part of the talk, I will indicate how VGIT can be used to provide a conceptual understanding of the (semi)stable locus in this quotient construction.<\/span><\/span><\/div>\n<\/div>\n<p class='mt-4'>Further information is available on the <a href=\"https:\/\/events.dm.unipi.it\/event\/153\/\">event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let G be a reductive group acting on a projective variety X.\u00a0 In Mumford&#8217;s Geometric Invariant Theory (GIT),\u00a0 the formation of a quotient in this situation depends on the choice of a G-linearized ample line bundle on X. In &#8220;Variation of GIT&#8221; (VGIT),&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/en\/eventi\/tba-lars-halvard-halle-univerista-di-bologna\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"template":"","tags":[],"unipievents_taxonomy":[],"class_list":["post-8179","unipievents","type-unipievents","status-publish","hentry"],"acf":[],"unipievents_startdate":1680105600,"unipievents_enddate":1680109200,"unipievents_place":"Department of Mathematics, Aula Magna.","unipievents_externalid":153,"jetpack_sharing_enabled":true,"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8179","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents"}],"about":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/types\/unipievents"}],"author":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":2,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8179\/revisions"}],"predecessor-version":[{"id":8531,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8179\/revisions\/8531"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/media?parent=8179"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/tags?post=8179"},{"taxonomy":"unipievents_taxonomy","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents_taxonomy?post=8179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}