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:20211224T113000Z DTEND:20211224T130000Z DTSTAMP:20260404T120402Z UID:LSAGIITM/10 DESCRIPTION:Title: The compactification of the universal moduli space of principal G-bundle s-3\nby Angel Luis Muñoz Castañeda (Universidad de León) as part of Algebraic Geometry at IIT Madras\n\n\nAbstract\nThese lectures aim to int roduce the problem of the compactification of the\nuniversal moduli space of principal G-bundles over \, G being a semisimple linear\nalgebraic grou p. I will explain recent developments on the subject based on Schmitt’s works\non singular principal G-bundles.\nAfter a brief introduction to the classical theory of principal G-bundles on smooth projective\ncurves\, I will 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 torsio n-free sheaf. When trying to construct a\nuniversal moduli space of singul ar principal G-bundles over \, a problem regarding the\nbehavior\, along w ith \, of certain numerical parameters (related to the objects and their\n semistability condition) show up. I will explain the recent results about this problem and\nstate the Existence Theorem of a universal projective mo duli space of semistable singular\nprincipal G-bundles over . This moduli space contains the universal moduli space of\nsemistable principal G-bundl es over M_g as an open subset. This condition makes the\nconstructed space a good candidate for an analog of Pandharipande’s universal\ncompactifi cation of the universal moduli space of vector bundles. This is part of jo int work\nwith A. Schmitt. If time permits\, I will speak about some open problems in the subject.​\n LOCATION:https://researchseminars.org/talk/LSAGIITM/10/ END:VEVENT END:VCALENDAR