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SUMMARY:Fine compactified universal Jacobians and their cohomology - Marco
  Fava\, University of Liverpool 
DTSTART:20240315T160000Z
DTEND:20240315T170000Z
UID:TALK209305@talks.cam.ac.uk
CONTACT:Alexis Marchand
DESCRIPTION:The Jacobian of a smooth proper complex curve X is the abelian
  variety parametrising of the line bundles on X. If we drop the smoothness
  hypothesis\, we can still define a generalised Jacobian\, which\, however
 \, fails to be proper. Constructing suitable compactified Jacobians is a c
 lassical problem\, addressed since the late '70s by Oda-Seshadri for a sin
 gle nodal curve\, by Altman-Kleiman\, Esteves\, Simpson and others for fam
 ilies of curves with planar singularities.\n\nIn particular\, a fine compa
 ctified universal Jacobian can be obtained by taking (stable) limits of de
 generations of line bundles on the universal family Cgn/Mbgn over the modu
 li space of stable curves of genus g with n marked points.\n\nIn this talk
  I will describe the geometry of a fine compactified Jacobian of a nodal c
 urve. Then I will use the topological stratification of the moduli space M
 bgn to show how to compute the cohomology of a fine compactified universal
  Jacobian\, using Hodge theory.
LOCATION:MR13
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