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CATEGORIES:Junior Geometry Seminar
SUMMARY:Fine compactified universal Jacobians and their co
 homology - Marco Fava\, University of Liverpool 
DTSTART;TZID=Europe/London:20240315T160000
DTEND;TZID=Europe/London:20240315T170000
UID:TALK209305AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/209305
DESCRIPTION:The Jacobian of a smooth proper complex curve X is
  the abelian variety parametrising of the line bun
 dles on X. If we drop the smoothness hypothesis\, 
 we can still define a generalised Jacobian\, which
 \, however\, fails to be proper. Constructing suit
 able compactified Jacobians is a classical problem
 \, addressed since the late '70s by Oda-Seshadri f
 or a single nodal curve\, by Altman-Kleiman\, Este
 ves\, Simpson and others for families of curves wi
 th planar singularities.\n\nIn particular\, a fine
  compactified universal Jacobian can be obtained b
 y taking (stable) limits of degenerations of line 
 bundles on the universal family Cgn/Mbgn over the 
 moduli space of stable curves of genus g with n ma
 rked points.\n\nIn this talk I will describe the g
 eometry of a fine compactified Jacobian of a nodal
  curve. Then I will use the topological stratifica
 tion of the moduli space Mbgn to show how to compu
 te the cohomology of a fine compactified universal
  Jacobian\, using Hodge theory.
LOCATION:MR13
CONTACT:Alexis Marchand
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