{"id":4884,"date":"2024-05-31T12:37:37","date_gmt":"2024-05-31T10:37:37","guid":{"rendered":"https:\/\/www.matematica.unina.it\/events\/prof-emanuela-de-negri-universita-di-genova-on-the-rate-of-generic-gorenstein-k-algebras-copy\/"},"modified":"2024-05-31T12:38:55","modified_gmt":"2024-05-31T10:38:55","slug":"prof-roberto-pirisi-brauer-groups-of-moduli-problems-and-enumerative-geometry","status":"publish","type":"ajde_events","link":"https:\/\/www.matematica.unina.it\/?ajde_events=prof-roberto-pirisi-brauer-groups-of-moduli-problems-and-enumerative-geometry","title":{"rendered":"Prof. Roberto Pirisi &#8211; Brauer groups of moduli problems and enumerative geometry"},"content":{"rendered":"<div>\n<p class=\"v1MsoNormal\">Il giorno\u00a0<b>6 giugno<\/b>, gioved\u00ec, il Prof.\u00a0<b>Roberto Pirisi<\/b>\u00a0terr\u00e0 un seminario presso l&#8217;<b>aula E<\/b>, III livello, con inizio alle ore\u00a0<b>17:00<\/b>.<\/p>\n<\/div>\n<div>\n<p class=\"v1MsoNormal\">\n<\/div>\n<div>\n<p class=\"v1MsoNormal\">Titolo:<\/p>\n<\/div>\n<div>\n<p class=\"v1MsoNormal\"><b>Brauer groups of moduli problems and enumerative geometry<\/b><\/p>\n<p class=\"v1MsoNormal\">Abstract:<\/p>\n<div>\n<p class=\"v1MsoNormal\"><b><span lang=\"EN-US\">The Brauer group, classifying Azumaya algebras up to Morita equivalence, is a fundamental invariant in number theory and algebraic geometry. Given a moduli problem M (e.g. smooth curves of a given genus, K3 surfaces, abelian varieties of a given dimension&#8230;) one can consider an element of the Brauer group of M as a way to functorially assign to any family X -&gt; S in M(S) an element in the Brauer group of S.<\/p>\n<p><\/span><\/b><b>If we consider the moduli problem M_g of smooth curves of a given genus, the Brauer groups of M_{1,1} (the moduli problem of elliptic curves) and M_2 are known over a vast generality of bases, for example Br(M_{1,1}) is known when the base is any field or the integers; the Brauer group of M_g for g at least 4 is known to be trivial over the complex numbers through topological methods.\u00a0<\/b><b><span lang=\"EN-US\">The case g=3 was until recently open over any base.<\/p>\n<p><\/span><\/b><b>In a recent paper with Andrea di Lorenzo (Universit\u00e0 di Pisa) we show that over any field k of characteristic zero the Brauer group of M_3 is equal to a direct sum of Br(k) and a copy of Z\/2Z.\u00a0<\/b><b><span lang=\"EN-US\">To our surprise, the proof of this result goes through one of the most well-known theorems in classical enumerative geometry: there are exactly 27 lines lying on a cubic surface in P^3.<\/span><\/b><\/p>\n<\/div>\n<\/div>\n<div>\n<p class=\"v1MsoNormal\">\n<\/div>\n","protected":false},"author":1,"featured_media":-1,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"tags":[],"event_type":[],"event_type_2":[],"class_list":["post-4884","ajde_events","type-ajde_events","status-publish","has-post-thumbnail","hentry","event_location-aula-e-al-iii-livello-del-dma"],"_links":{"self":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/4884","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events"}],"about":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/types\/ajde_events"}],"author":[{"embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4884"}],"version-history":[{"count":2,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/4884\/revisions"}],"predecessor-version":[{"id":4886,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/4884\/revisions\/4886"}],"wp:attachment":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4884"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4884"},{"taxonomy":"event_type","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type&post=4884"},{"taxonomy":"event_type_2","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type_2&post=4884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}