BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicola Pagani (University of Liverpool) DTSTART:20200820T150000Z DTEND:20200820T160000Z DTSTAMP:20260423T052923Z UID:ZAG/42 DESCRIPTION:Title: Cla ssifying fine compactified universal Jacobians\nby Nicola Pagani (Univ ersity of Liverpool) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\ nAbstract\nWe introduce the notion of a fine compactified Jacobian of a no dal curve\, as an arbitrary compact open subspace of the moduli space of r ank-1 torsion-free simple sheaves. We show that fine compactified Jacobian s correspond to a certain combinatorial datum\, which is obtained by only keeping track\, for all sheaves\, of (1) the locus where it fails to be lo cally free\, and (2) its multidegree. This notion generalizes to flat fami lies of curves\, and so does its combinatorial counterpart. When the famil y is the universal family over the moduli space of curves\, we have the fo llowing results: (a) in the absence of marked points\, we can fully classi fy these combinatorial data and deduce that the only fine compactified uni versal Jacobians are the classical ones (which were constructed by Pandhar ipande and Simpson in the nineties) and (b) in the presence of marked poin ts there are exotic (and new) examples that cannot be obtained as compacti fied universal Jacobians associated to a polarization. This is a joint wor k in progress with Jesse Kass.\n LOCATION:https://researchseminars.org/talk/ZAG/42/ END:VEVENT END:VCALENDAR