{"id":3170,"date":"2023-08-31T22:38:08","date_gmt":"2023-09-01T05:38:08","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=3170"},"modified":"2023-08-31T22:38:08","modified_gmt":"2023-09-01T05:38:08","slug":"cellular-resolutions-of-the-diagonal-and-exceptional-collections-for-toric-d-m-stacks-reginald-anderson-cmc","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/cellular-resolutions-of-the-diagonal-and-exceptional-collections-for-toric-d-m-stacks-reginald-anderson-cmc\/","title":{"rendered":"Cellular resolutions of the diagonal and exceptional collections for toric D-M stacks (Reginald Anderson, CMC)"},"content":{"rendered":"<p>Beilinson gave a resolution of the diagonal for complex projective space, which gives a strong, full exceptional collection of line bundles as a generating set for the derived category of coherent sheaves. Bayer-Popescu-Sturmfels generalized Beilinson&#8217;s resolution of the diagonal by giving a cellular resolution of the diagonal for a proper subclass of smooth toric varieties which they called &#8220;unimodular.&#8221; In joint work with Gabe Kerr, we extended this resolution of the diagonal to smooth projective toric varieties by showing that the cokernel of Bayer-Popescu-Sturmfels&#8217; resolution is torsion with respect to the irrelevant ideal. In this talk, we show that Bayer-Popescu-Sturmfels&#8217; resolution yields a strong, full, exceptional collection of line bundles for unimodular projective toric surfaces, and that our extended resolution of the diagonal yields a strong, full exceptional collection of line bundles for a smooth, non-unimodular projective toric surface.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Beilinson gave a resolution of the diagonal for complex projective space, which gives a strong, full exceptional collection of line bundles as a generating set for the derived category of [&hellip;]<\/p>\n","protected":false},"author":73,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[13],"class_list":["post-3170","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - 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