BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Angel Luis Muñoz Castañeda (Universidad de León) DTSTART:20211210T113000Z DTEND:20211210T130000Z DTSTAMP:20260404T120001Z UID:LSAGIITM/8 DESCRIPTION:Title: The compactification of the universal moduli space of principal G-bundles -1\nby Angel Luis Muñoz Castañeda (Universidad de León) as part of Algebraic Geometry at IIT Madras\n\n\nAbstract\nThese lectures aim to intr oduce the problem of the compactification of the\nuniversal moduli space o f principal G-bundles over \, G being a semisimple linear\nalgebraic group . I will explain recent developments on the subject based on Schmitt’s w orks\non singular principal G-bundles.\nAfter a brief introduction to the classical theory of principal G-bundles on smooth projective\ncurves\, I w ill introduce the notion of singular principal G-bundle. Such objects and their\nsemistability condition can also be introduced over stable curves\, and generalized by\nallowing the underlying vector bundle to be a torsion -free sheaf. When trying to construct a\nuniversal moduli space of singula r principal G-bundles over \, a problem regarding the\nbehavior\, along wi th \, of certain numerical parameters (related to the objects and their\ns emistability condition) show up. I will explain the recent results about t his problem and\nstate the Existence Theorem of a universal projective mod uli space of semistable singular\nprincipal G-bundles over . This moduli s pace contains the universal moduli space of\nsemistable principal G-bundle s over M_g as an open subset. This condition makes the\nconstructed space a good candidate for an analog of Pandharipande’s universal\ncompactific ation of the universal moduli space of vector bundles. This is part of joi nt work\nwith A. Schmitt. If time permits\, I will speak about some open p roblems in the subject.​\n LOCATION:https://researchseminars.org/talk/LSAGIITM/8/ END:VEVENT END:VCALENDAR